Are they IDE or SATA?
Look in the BIOS, and see if you have a slave or secondary channel. If so, is the 2nd drive showing in there (with the 1st drive also connected)?
It's possible that your power supply is that stressed out, that an additional drive is too much for it. A hard drive doesn't consume that much power, but it is possible. What model of PSU do you have? What are your other hardware components?