GE top loading washer basket won't spin.
The center thing spins, the water drains but the basket won't spin. Washer was Purchased in 2003.Answer
The first thing you need to check is the hub nut and the hub. Pull the agitator off (it just pulls straight off) and remove the agitator coupling (it is held on by a 7/16 bolt). Then you should see a big nut that holds the basket in place. If that nut is loose you will need to tighten it. There is a tool called a Spanner Wrench
(Click on link to view and/or order) that is used to tighten that nub. Use it with a hammer to tighten it. This page has a picture of me useing that spanner wrench GE Washer Disassembly
Sometimes I see the hub actually break out if this is the case once you remove the agitator it will be obvious. The spin basket will have to be replaced if that is the case.
If the hub nut isn’t loose and the hub isn’t broken the transmission is bad. The link above will help with replacing the transmission.
Scotts question was answered here Washer Won’t Spin