You might want to give the actual Model & Type numbers from the engine so we can see what you actually have.
127CC is about 8 CI. I have over 30 8CI Briggs engines in my "Briggs folder".

What do you mean by manually primed? Pushing a primer bulb or actually removing the spark plug and dribbling a bit of gas into the cylinder? (or something in between)

Here's what I could read from the pull started cover:

Model 80202
Type 1765 01 850516 xxx (the final numbers were not readable unless I pull the cover).

I put a small amount of fuel directly into the air inlet which usually works. It hadn't been started in over one year, so that worked the first time.

Thank you for the help.

"I put a small amount of fuel directly into the air inlet which usually works. It hadn't been started in over one year, so that worked the first time."

That's a bit confusing. Is it running now?

That's a pretty old engine, (May 16, 1986)

Typically when you have carb problems on these it's either the fuel pick up tube is clogged or the diaphragm is bad (Briggs part# 270026)
It's located under the little side cover with 3-4 screws.
Also under this cover are a couple "ports".
IF you replace the diaphragm, it's a good idea to use some carb cleaner and force some carb cleaner through the ports with the "plastic straw".
One should cause a bubbling sound in the tank and the other should blow through to the venturi area of the carb.

Unfortantly, the fuel through the inlet only worked once. When I went to restart it, that's when I had the problem. I will try cleaning the carb. Can you think of any other potential area to look at? Also, is 75 #'s of compression good for this old motor?

One thing it is doing, and I don't know if this means anything, is that it seems to be giving me a slight pop-back through the carb; not like a backfire, but a slight puff; it may be normal, I just thought I would mention it.

Thanks again.

I already gave some LIKELY areas to look at!
Why mess around with "potential" areas until the obvious areas are checked first.
A new diaphragm is maybe $3-4 and just about any place that works on this type engines will have several in stock because they get used OFTEN.

I rebuilt the card including soaking in carb cleaner for 48 hours, all passages blownout with carb cleaner and then compressed air, new diaphragm, new gasket (between the carb and the fuel tank); tank cleaned, fresh fuel, new spark plug; can't get even a whimper from it. Thoughts?

Have you checked for spark?

At this point, I would check for a sheered flywheel key. You don't say if you hit something before all this started.