The graphics card shouldn't be directly affecting your other system hardware besides obviously drawing too much current! but that seems not to be the prob...
The most damage a 'dead' gpu would do is cause a failure to boot or a conflict with another piece of hardware due to bios settings.
Can you access your optical drive in dos/linux/a 2nd version of windows (if you dualboot)or any other alternative os?
If so, then its a driver/api/dll issues in windows. Quickest and cheapest way would be to wipe and reinstall from scratch. Or, if you still have your old card, reinstall that to see if the issues has been fixed. If it isn't then maybe your drive is faulty.
If not (from above) then its either a dead optical drive, or some BIOS setting which is incorrect. Having not ahd this problem, all i can suggest if looking in the bois is checlking PCI/Pnp config, hardware assignments/irq, disabling any "graphics turbo boosters"
A friend of mine often had optical drives going missing and it turned out that replacing the PSU with a more powerful quality one solved that problem.
As you say this has started happening since you've installed a new (presumably more powerful) Gfx card, it is possible it may be a PSU issue.
If you have more than one HDD, Optical drive or any other device that draws power from the PSU, temporarly disconnect anything that you can do without so you can test to see if the optical drive still disappears.
