Hi, I realize that the problem described in the subject may seem deceivingly simple to solve, however realize that it is not the case:

I have a Dell Dimension 8400 desktop with Windows XP Home Edition. I was attempting to reinstall Windows on it, however I could not get the computer to boot off of the disc. Thinking that I might be able to start the setup from within Windows, I booted into Windows only to find that BOTH optical drives cannot read discs (as in, they both tell me to insert a disc even though there is clearly a disc in the drive). The drives also appear in the BIOS, but cannot be booted off of either. And yes, I'm certain the discs are bootable, and even if they weren't, it would still be recognized in Windows.

Also, I ran Dell's (simplistic) diagnostic tool and it asked me to insert a data disc so it could run tests on the optical drive, except there were already 2 discs in both drives.

I have also double checked all cable connections inside the case, all are solid, and I have already flashed the CMOS. I have also updated to the latest (Dell provided) firmware updates for the BIOS as well as both optical drives. Any suggestions?

The Dell Dimension 8400 is at least four years old... or more.
Several of the 8400's came with HL or HLDS optical drives, which failed early and often. Yours are likely long dead. What you describe is typical of a failed CD or DVD drive for which the reader lense has burned out or the drive has slipped out of alignment dut to wear.
Luckily, optical drives (DVD-RW and CD-RW) can be found cheaply online for $19.94 US to $39.99, and are relatively easy to install. We recommend Plextor (costly but great), LG, Samsung, LiteOn, or Pioneer. I would avoid Sony, Sony Nec, Sony Optiarc, HP, Acer, Asus, HLDS, Arctec and Rosewill as they do not seem to last as long in our computers.