You should call or visit your local Sears parts shop with all of the numbers that you can find on your mower.

Thanks anyway. I have scoured this thing from top to bottom, it's pretty clean actually but I can only find the Briggs & Stratton number on the heat shield but nothing on the mower or bag or anywhere inside, under the bagger flap...nowhere. Our Sears repair place in town closed years ago, not even sure where one is now. I was inquiring here to see if anyone knew of a website where I might research it and maybe do a visual identification and then find the part.
I got the rear axle off this morning, took the 7 torx screws out of the gear box but you can't crack it open. It's glued together with a really strong sealant. I can turn the pulley and it kind of turns the axle but doesn't seem to turn the wheels so it may be stripped at that end too.
Anyway, it has hit the point of diminishing returns for me. Need to get on to other projects now. I'm screwing it all back together and storing it until I find another mower with a blown engine possibly or it's going in the next yard sale for 25 bucks.
Thanks for the advice.

http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=180493860631&ssPageName=STRK:MEWNX:IT

Does the gearbox look like that from the top? On the bottom it has straight rows of ribs. Bolts enter from the top on this model. This was a very common gearbox.

http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=180493860631&ssPageName=STRK:MEWNX:IT

This was a very common gearbox. Does it look like this? The bottom was all straight ribbed fins and the bolts entered from the top.

I presume you've checked with http://www.searspartsdirect.com -- they may be able to assist.

And by all means, take a picture of the gearbox and mower and post them in this thread -- baymee is correct that most Sears mowers use very common parts, so chances are somebody will be able to ID the gearbox or the mower.

Here is a link that might be useful: http://www.searspartsdirect.com

I want to thank everyone for the great advice. If I decide to pursue this further I may try and post a pic of the gearbox if I'm sure it is the gearbox or send Sears or a parts dealer a photo of the part.
The gears that drive the rear wheels via the grooved inside wheel rim seem like they have a clutch or ratchet I guess to allow the mower to roll faster than the drive shaft when pushed or going downhill. Is there some kind of ratchet or friction plate between the gear and the shaft that can wear out or is still more likely to be a shot gearbox?
Anyway, the left rear wheel is cracking also and has a flat spot so when I looked up a replacement for that it may cost between 18 and 25 bucks plus S&H and if this driveline or gearbox replacement ranges around 80 bucks plus shipping and handling I'll be almost halfway to the cost of purchasing something like a brand new Troybilt with a Honda motor that is lighter and quieter. This will most likely just stay a push mower with an intermittent driveline to be used as a an emergency spare. Cost of that route = 0 Dollars. Or placed in the next yard sale with a sign reading 30.00 obo.
I may also find another cool project for a kind of heavy/noisy 7HP B&S someday.