Well, since it's an engine problem you might tell us WHAT engine it has.
BRAND -- Model -- Type/spec

hmm, and here i thought i was giving enough info. sorry. but as i stated in the begining of my post, i know very little about this. also i won't be home to look at the engine for a few days. but i did find stuff by searching the model number i gave...
parts list...
http://www.searspartsdirect.com/partsdirect/part-model/Ariens-Parts/Riding-mower-tractor-Parts/Model-93604200/3071/1509200

from what i remember the engine is a Briggs & Stratton. maybe 20hp...
http://forums2.gardenweb.com/forums/load/tractor/msg061533474751.html

lotsa stuff...
https://www.google.com/search?q=Ariens+model+93604200&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a#hl=en&sugexp=les%3Beqn%2Ccconf%3D1.0%2Cmin_length%3D2%2Crate_low%3D0.030%2Crate_high%3D0.030%2Csecond_pass%3Dfalse%2Cnum_suggestions%3D2%2Cignore_bad_origquery%3Dtrue&gs_nf=1&dc=model&gs_mss=Ariens%20m%2093604200&tok=p5l6U4_mntt9tyOkjtRPmg&pq=ariens%20model%2093604200&cp=7&gs_id=4dz&xhr=t&q=Ariens%20%2093604200&pf=p&client=firefox-a&hs=p9F&rls=org.mozilla:en-US%3Aofficial&sclient=psy-ab&oq=Ariens++93604200&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=4e6826f2b8c33834&biw=1342&bih=551&bs=1
again, advice much appreciated!

thank you Tom for your reply! yeah the strange thing w/ the Starter fluid is i thought usually an engine would only run a short while until the fluid burned off? but w/ just a short spray, this mower ran for a long time. it ran setting for about 10 minutes, then i even rode it around about 1/4 acre. didn't engage blades tho. but it ran for like 20 minutes until i finally shut it off. but then wouldn't start again. won't start after cooling off either (hours-days).

I best read closer the next time. Yes, if it would ONLY run on starting fluid- then I would think something like water in the fuel. I assume that when it runs that all sounds normal? No abnormal emissions? Maybe run the deck up next time and see if the power seems normal or not.My first two thoughts would be to verify that the choke is working and fuel is reasonably fresh. Fresh as in like within a couple of months from purchase? Let's start there.

welp. we thought we had it fixed. used the Starter fluid to get it running, then periodically would spray Carb cleaner into it every few minutes. cut my entire 1/2 acre lot like this. stopping every 15 mins or so to spray in some carb fluid. then shut it down, and let it cool off for couple hours. and then it started right up. so we cut my neighbor's 1/3 acre lot lol. did not stop to spray any fluids this time, and had the air filters and cover back on. again, i shut it down for hours and it would still start. seemed fixed.

3 days later, it's back to the same thing. won't start without starter fluid. could it be some sorta sticky residue that loosens up when it's running and hot. but then dries when cooled down, and sticks the carburetor shut?

Add a few ounces of Seafoam to both the oil and fuel then run it up for a spell and see if your theory is correct. Again, be sure fuel is fresh. Fuel pump could be suspect. Engine #s could help.

I have an Ariens lawn tractor (model 93604200) that is doing the exact same thing. Won't start when cold. I can prime it with some gas or starter fluid, it will start and run fine. As long as the engine is still warm, it will start back up. After it sits and gets cold, it will not. Spark is fine. Please post back if you find out what's wrong with yours, and I will do likewise!

so sorry to hear that Kenny! maybe we'll get somewhere w/ this.
Tom, could not find numbers on engine. i read that they should be on top side of square silver thing mounted on side of engine. nothing i can find. but a service rep said it's this...
Model #406777-1404-G1 Briggs & Stratton Engine
http://www.searspartsdirect.com/partsdirect/part-model/BRIGGS-STRATTON-Parts/All-Products-Parts/Model-4067771404G1/1245/1503500?pathTaken=&prst=0amp;shdMod=406777-1404-G1
i tried the Seafoam 2 different times. start w/ starting fluid, run around 1/2 yard for 40 minutes, but unlike the 1st time which started again after turning off (even an hour later), these times it would not start right after shutting down. don't think it's flue pump either as i bought new fuel filter and when changing, fuel came out both sides of tube. also after filter installed it filled up rapidly w/ gas after tractor started (w/ spray).
gawd just hope the engine doesn't need a total rebuild or something!

If tractor runs with starting fluid I would doubt that an engine rebuild is necessary. I am not familiar with that engine, but looking at the carb in the link you posted it has a main jet inside the bowl of the carb. If the gas was old and sitting in can or tractor, I would disassemble the carb and spray it with carb cleaner ( not starting fluid). Gas will turn to varnish like when it sits and gum up jets. Spray all holes(jets) and make sure nothing is blocked. Clean the bowl itself and the needle value that is connected to the float. Take care removing parts and remove over clean work surface to not loose parts. Make sure the control cables are put back.
2) You mentioned that the air filter was covered in oil. If this is a paper element, replace it. I had a honda engine that ran very rich and finally replace the oily filter(even thou it looked clean) and it ran like a champ.
3) General rules -- engine needs two things to run, spark an gas. you have eliminated spark, hence I strongly feel you should check the carb, since you have already checked hose.

Good luck.

just wanted to update this since it's turned into THE WORST EXPERIENCE EVER as a consumer! close to a year, much money, and much labor later, this damn thing still won't start on it's own.
first we had a neighbor who works on cars professionally take a look. he did a lot of work on it. then we had a pro tractor repair service get on it. so far it's had all the things suggested in above posts (Seafoam, new gas, plugs ect), gas tank taken off and completely cleaned, electrical checked, new fuel lines, new fuel pump, new filters, carb taken apart then a brand new carb (pricey!), new governor springs (wth is that??), idles checked. the service says they're gonna try a tachometer next, and then they sound like they're about to give up lol. i mentioned i probably won't pay for a total engine rebuild. as it stands, we've spent over $500 and damn thing still is EXACTLY as it was when i 1st made this topic. it will only start w/ starter fluid, except back then it would stay running for however long you wanted. now it cuts out sometimes.
worst experience ever. remember, all this started 6-8 WEEKS after the warranty expired. i shoulda contacted Home Depot then, because in the past i'd had something break shortly after the warranty (Xbox) and the seller worked with me. but i figured Home Depot would not. i still shoulda tried.
anyway DO NOT BUY AN ARIENS!

Contaminated fuel could be causing the problems that you are seeing with this lawn tractor. Would it be possible to test your fuel in another small engine, like a lawn mower? If the engine will start and run evenly on starting fluid, then the engine does not need to be taken down and overhauled. If it is using oil or smoking that is another matter, but you do not mention any symptoms like these. We have an Ariens snowblower, with a Tecumseh engine, that starts easily, even when cold, and runs reliably. It has an electric start feature that I have never bothered to use, because the hand pull is more convenient. Engines are not that complicated, you just have to hang in there and locate the source for apparent fuel starvation.

If the mower runs normally once started with a shot of starter fluid. The problem is with the carburettor. Push comes to shove, if starting fluid does the job well enough to allow usage ...I would get a can of Chem-tool B12 cleaner and a qt of MMO . Less than 10$ at an auto parts store. I would also install a shut off in the fuel line. This activity would have drained the tank . Add fresh, just from the pump gas. First put 4 oz of B12 and a capfull of MMO in then fill. When you are done mowing, park it and turn the shut-off off. After every use run the carb dry.

Hi.

I think I finally found the culprit for my 46" cut Mower.... The throttle cable slips 1/4"...

Before starting, I opened the hood, put the choke on and gave the cable a good tug, pulling away from the engine... sure enough, it moved, opening the throttle up a bit more. Fired right up without issues.

Tried tightening the cable stay, but it didn't do much... slipped again by my next mowing.

Give this a try, let us know if it works!

I have an ariens riding mower that was having all the same problems. I tried the throttle cable as one submitted. It worked! I pulled on it and the mower fired right up and I was able to mow today! After hours of frustration over several days I asked the Good Lord himself for intervention. Within an hour he lead me to some great advice. Thanks..... JC.

Same thing for me, adjusted the throttle cable and it fired right up (after a few days of looking at other stuff). Thanks for the tip above because that is how I fixed it. The only way I could start it before was jumping it from my car.

I had another issue last year, it wouldn't start because of the gas cap. I couldn't find a vented cap that fit right so I drilled a small hole through the top of the cap, worked great. I've had this mower for 5 years, once it dies I will never buy an Ariens again. Should have went with John Deer or Cub Cadet.

Ariens 1742 -- Mine will crank forever and act as though it's being flooded... The fix my dad came up with and I used is clamping a spring clamp on the black fuel line hose (on the right rear) to restrict flow and it fires right up, at which point I remove the clamp and it continues to run normal... I realize I'm late to the party for this answer but maybe it'll help someone sometime 🤷🏿‍♀️