when i put a cd rom in my drive, the drive makes a few short screeching noises. then i get a error message. when i open the tray i see that the cd rom did not spin. is the drive trash?

Most likely, yes. If the disc didn't move then the problem is probably in the drive system and, at the price of drives today, not worth attempting to repair.

CD-ROM drives are easy to change...

If you're at all handy with tools, changing a CD-ROM drive is very easy to do. This page has step-by-step instructions:
Installing a CD-ROM

I hope this helps!