Nope, the working drive will not break in the non-working computer as far as i know, i dont see any possible thing that could make it do this.
But even by chance that you kill it, which is highly unlikly, they are VERY cheap to buy. So dont sweat it, go mad, take it out and put her in the broken computer, and follow the steps i listed above, should work out fine for you. if not post here and we will see what to do from there
P4 2.5 Ghz/socket 478/400FSB/512L2
512 megs PC800 Rambus
ABIT TH7II-Raid mobo
128MB Nvidia FX 5200 Home Theatre w/TV out and Remote
80 Gig Western Digital/8mb Cache/7200 RPM\'s
20 gig Fujitsu/2mb Cache/5400 RPM\'s