Some thoughts:
1. What password are we talking about? It can't run Mac OS 8 or 9 or X, so if you are getting a password prompt, it might be the program named At Ease that was often used for security under Mac OS 7. What exactly does the login screen look like?
2. You can defeat the At Ease password if you have the At Ease installer on any compatible media (floppy or CD-ROM). I think At Ease even came with the Performa originally, but I'm guessing you don't have the disks that came with it, right?
3. If all you need to use the CD-ROM drive is a disk tray, might you be able to find one on eBay or at a local Mac store? I think you'll be much happier if you can use the CD-ROM drive. If you can get it working, you might want to start clean and re-format the disk and install your own Mac OS on it. As a side effect, this would wipe clean that password (and everything else on the disk). Mac OS 7 is free. You can download it from Apple. I, or another member, can find the right URL if you want it. Or you can probably find a Mac OS 7 installation CD-ROM on eBay.
4. Do you have any other similar Macs? If you, you could, in theory, swap the Performa's hard disk into another Mac, install the O.S., and swap it back.