I have a set of 500E Diagnostic CD's that will no longer boot up. The old computer that I previously used died years ago and my new computer apparently does not have the proper software to operate them.

Can anyone provide me with some guidance?

It might help to identify what the old computer was running, versus the new, and also be a bit more specific about the software.

For instance, was the old computer running Windows 3.0, NT, Win95, 98, SE, ME (anyone getting nostalgic yet?), 2000, XP . . .

Typically, the issues with the CDs or DVDs from Mercedes, if that's what you're using is that that they need older drivers, are not compatible with 64bit OS (possibly even 32bit) or with non-MS systems.