Cassette Deck Help?

Does the tape advance in 'play' or still ?
Inspect the pinch roller and its drive belt. If advances, check the audio path, amplifier, headphone insertion switch.

 

You will have to take it apart and see if the belt is moving both pulleys it's on, or if the motor is stalling, or pinch roller not staying on, hardened rubber or broken spring, etc.

Is the player worthy of buying parts for? You might find something that works, cheap at a garage sale, craigslist, or pawn shop, or sometimes I shop for *local* (pickup) items with no reserve auctions on eBay. Last bookshelf stereo I got for $0.01... but without the remote control, which I ended up paying someone else $10 for.

 

Sounds like the belt to me, you've got good advice already from others here.
My additional input is to use a Q-tip and some rubbing alcohol and clean the tape heads.
The build-up on the heads is another drag on the tape travel, ... although I'm with the other guys
here that you probably need a new belt.