I finally put together the P3 system in my signature:

Gigabyte GA-6OXT
Pentium III 1200
3x128MB PC133 RAM
MSI GeForce 3 Ti 200
Diamond MX300
10/100Mbit Ethernet

Every part aside from the GeForce 3 in this system is tested to work in another PC, and I have no reason to believe the GF3 is faulty, though I will try with a known working graphics card tonight regardless.

When I turn the PC on, it seems to get stuck in a boot loop; the hard drives and CD-ROM spin up for a moment, then slow down, then up again, then down - this goes on for a few seconds until I get a continuous, rapid string of short beeps from the PC speaker that never ends: "BEEPBEEPBEEPBEEPBEEPBEEPBEEP..." - almost no pause in between, very short and rapid beeps, and continuous.

The BIOS is labeled as Phoenix BIOS on the chip. I could not find a Phoenix BIOS code for this kind of behavior, however this Gigabyte FAQ I found when googling says continuous short beeps are Power Supply Failure related. This PSU was working fine with a GA-BX2000/PIII-700/GF2GTS configuration, but it's a No-Name (read: shitty) 380W (It is feather light so I SINCERELY doubt it is actually properly rated for little more than half of that, if that) so I have pulled it out, and I will be trying a FSP 300W Athlon era PSU with strong 5V rails tonight.

Other than that, I'm kind of stuck for ideas, and would be open to suggestions..