Hmmm...
Only 4 Ideas come to my mind :
1)
Check Bios settings.
The Problems you described, are possible when some Video Related Options are set within the Bios. Disable Video Bios Shadow, Fast Writes, Video Bios/RAM Cacheable, Write Combining, Palette Snoop etc...
Basically check that all that could affect the Card is set to "safe" and conservative Values. Voodoo's have traditionally been quite tolerant to many Bios Settings, but it's worth a shot.
2)
Check the Integrity of the Card itself.
e.g. check for popped/malformed Capacitors, or disconnected/broken components.
Sometimes, those can actually break their Connection to the PCB, while being extremely hard to see or detect. Note that Capacitors should always stand upright from the PCB (often enough, one finds those slightly bend to one side)
3)
Check Video RAM.
I know the C'T Magazine released a Video RAM checker (basically a "Memtest86" for Video Memory, which actually runs from Video RAM as well, quite a unique Program).
I'll have to search for the Program, and will post a Link when I find it.
If the VRAM is broken, just about anything can happen.
Often, in low Resolution and Color Depths (when only a tiny part of the VRAM is actually used), the Card works fine, but as soon as higher Resolutions and Color Depth is selected, the Framebuffer encloses the defective RAM Area as well, usually crashing the System.
4)
Check the Card's Temperature.
I transitioned quite a number of Voodoo3's from one System to another, just to find out it was all of a sudden running
lightning hot (!).
I actually had to remove my Voodoo3-3500 because of that; even big quality Fans I put onto it basically had their bearings "burned out" within a few weeks
A Voodoo3-3000 should he quite warm upto hot, but never too hot to touch. Unfortunately, a Voodoo3 commonly even then runs (for a while) with no apparent Problems, until it suffers permanent damage.
(my V3-3500 made it over several months, before I noted it was burning hot. Unbelievable it still lived after this hell it was going through
)
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About Power consumption :
The only Motherboards/Chipset in know of, that had actual Trouble to feed a Voodoo3 (or TNT1) with stable Power, was the Socket7 Ali-V (Alladin) series. (several Tweaks/Patches exist for those combinations however)