If your computer was manufactured by a proprietary makes such as Dell or HP, it normally comes with a hardware diagnostics utility that should help find any hardware that has gone bad.
I have an HP Pavilion desktop that has been plagued with startup issues that had me tearing my hair out. In the end I ran a full diagnostic test, which the DVD-RW/RWW failed.
If you have it, run the diagnostics. If not, do you know anyone who has a spare optical drive you could try?
Even if you have to buy one, they are not very expensive these days.
Check here for diagnostic software:
Downloads - Optical Drive Diagnostics