I would wonder if your PSU was at the edge of its capacity. Isn't it the case that when you boot, both your DVD drives spin-up (noisely) for a couple of seconds? That's a simultaneous max-power-load from both DVD's, if so. You could test this by dropping other power-loads to see if that allows both DVD's and a successful boot: disconnect all (non-cpu) fans and pull any unnecessary (for boot) cards [such as sound, NIC, SLI'd GPU, TV-capture, etc.]. If reducing the power-load from other devices let's the system boot w/ 2 DVD's, buying a newer/more-capable PSU is an obvious solution.
You haven't specified the cabling method: on an IDE cable, there's a slight chance the cable could have some defect: swap with another cable just to check it. This is pretty unlikely.
Once upon a time, BIOS's had the option of sequenced powering-up HD drives. That might also have included CD/DVD drives, but I never needed it. The purpose was to avoid the simultaneous power-demand of all the drives starting at once. I haven't looked into this of late, but it might still an obscure BIOS option. [Since I -haven't- noticed it for several years, I doubt it still exists, however.]
Good luck!