First: Make sure the + cable of the battery goes to the starter, through the solenoid connections, and the ignition switch. and the - cable goes to the frame of the tractor. Those marks are on the top of the battery. The (+) cable is usually red, and the (-) cable is usually black.
At this point, if you are seriously confused, might i recommend that you seek professional help! I say this, because, if you don't know where the starter is, or what it looks like, you will probably be taken for a ride by unscrupulous individuals, which will cost more money than if you take it to a reputable lawn tractor/mower repair shop!
In view of my being a lawn mower fixer, and not a Dr., I can truly say that lawn mower fixing is not unlike being a Doctor! We have to deal with mower owners who will be quite upset when we tell them their machine is either un-fixable, or just ready for the scrap heap.
It is extremely difficult to try to advise somebody thru this medium, especially when they don't know what the starter looks like, or its location! My advice to you is to seek a repair shop and let them fix it so it is usable. Cheaper in the long run.

Thank you Rusty for your quick response. After I wrote the post,I began to think like you regarding the starter,etc. Am making arrangements to have it p/u and repaired. docrx

When you seek the professional shop to address the problem, it's best you don't go in there and declare you are having trouble with your starter, or worse...........that you think you might have a bad starter. Either of those declarations could be taken as an authorization for the shop to replace the starter without testing anything first, and if/when that does not solve the problem, you might be told that you have some other problems IN ADDITION TO the bad starter.

You need to just tell them your engine is not CRANKING properly when you try to start it.
Tell them you replaced the battery "a while ago" (I still haven't been able to determine how long that is).

Mownie is SO RIGHT. Tell the service tech what the machine does (or doesn't do.) I'm "middling" good at fixing things, but I frequently find that what I thought was wrong turns out to be something else.

In your case, I SUSPECT a grounding problem much more than a starter malfunction. If you hadn't already turned it over to a tech, my first recommendation would have been to check that both battery cables are FIRMLY attached at each end.

Thank you for all the replys. All of you gave great advice. My neighbor is a retired policeman that likes to tinker with motors. I bribed him with a 6 pack if he would look the engine over,etc. He found a loose wire,hooked it up and it started. thanks again for you advice. docrx