My CD ROM drive (drawer) will not open. Does anyone know what might be causing this problem?

The springs that eject might be caught... stick a paper clip in the tiny hole to open and check the reader...

There can be several reasons for this beside a broken drive. Is there a disk in the drive? I once had a drive that held the disk in play position because the magnetic holder came loose from the spindle. There are two holders, one above the disk that's free floating and one below attached to the drive shaft. When you put a disk in the drive the one below rises up to connect to the free floating holder magnetically to hold the disk for spinning. It's supposed to drop back down when you hit eject but if it comes loose from the spindle it just hangs there and the drawer can not open. I had to take mine apart and press the lower holder back on and it never came off again. If this is the case (unlikely) using a paper clip to open the drawer will fail as it did for me.

When was the last time it worked? Is there any CD inside the CD ROM? Most of the time it could be physical problem.