My Roper dryer that is about 8 years old was making a screaching sound for a couple days but still drying. While it was drying a load of clothes it suddenly completley stopped working and made a horrible burning smell. What could be the problem?

Without model numbers I can't give you a specific answer, but my guess is that the drum bearings have gone bad.

The squeak was the warning, and now with a complete lock-up, the drive belt slipped on the drum, causing the burning (rubber) smell. Note: If the burning smell is electrical instead of rubber, you may have additional problems (electrical).

Inspect the drum bearings and drive belt (and idler pulley, if you have one), and see if they are stuck. You might be able to lube them a little to verify that once they move you'll be okay, but I would replace them if that works! You're really just verifying that you don't also have an electrical issue that was caused by the bad bearings.

Hope this helps,
WallyH

It sounds like you have the problems noted above plus it is extremely dirty. If you will tear it down you will see the problem and be able to fix it.