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Ironically, it's the same Tabor III motherboard that I spoke about before, although this problem is very strange. For some reason, the computer would not boot from any bootable CDs, even official Microsoft ones. It had a black DVD-ROM/RW/R drive from 2001 in it (it didn't match with the beige case, but there were many features including CD writing stuff that I wanted, and it was an older drive). I tried testing official Microsoft CDs that were known to be bootable, and nothing. I even tried using the all in one boot disk to run a boot loader, and the boot loader didn't even see the DVD drive, even though it was properly connected.
Fast forward to now, and I changed the IDE cable to a known working one, and changed out that DVD drive with a known working beige CD-ROM drive. The Windows 95 boot disk (official) was able to recognize the CD drive and I was even able to get a directory view out of multiple CDs.
I ran into this problem the moment I got the system set up, actually; I didn't really worry about it though, as I was able to use the trick where you copy the win98 installation files to a directory on the HDD and start it from there. The DVD drive ran fine under Windows 98, never got a single read error or anything, and I installed Half-Life, and both CDs of Microsoft Office 2000 on it.
Windows 98 was crashy when starting Half-Life, so I decided to try Windows NT 4.0, where I ran into this problem. I tried using the all in one boot disk to boot the CD, but it didn't list it. I even went as far as to get the three Windows NT 4.0 floppy disk images written onto three floppies, but that setup said that there was no CD drive installed at all. This was both with the DVD drive and CD drive.
I'm running a RAM test right now, because at this point it's the only thing I could think of, and bad RAM is even far-fetched. I don't understand what is going on, as I have went through each and every possible culprit to no avail, even going as far as to switch the molex cable connected to the DVD drive with a different one. Same results.
I forgot to mention that both the DVD and CD drive are detected in the BIOS just fine. It lists them at the initial bootup screen and at the BIOS setup screen.