I have a Voodoo 4 4500 AGP card that is working intermittently on two different systems that worked fine with other AGP cards.

Sometimes I only get a black screen and no video or motherboard POST.
Sometimes I only get a Video and motherboard POST then blackness.
If the video and motherboard post, I can get into the BIOS settings.  

When I do see a video POST, every other letter is flashing on and off.
Also, when motherboard POSTING or in the BIOS, I see thin vertical lines on the screen.

So then I try to update the V4 4500 BIOS.  I install a nVidia FX5500 PCI card and boot with that card as primary, then I load a DOS startup disk and then run then flash utility with BIOS 1.15.  So the Flash program begins to setup and I get a message: Unable to identify board.  The flash program just stays at this message screen.

Ok, so now I ran PCI.exe that Hank recommends to figure out if your card is nuked.  

"Boot to DOS, then execute PCI.EXE. You should see several devices, the ones you are looking for are 121Ah (3dfx). If you see the device then your card is alive and just the BIOS is nuked. If you do not see the 3DFX signature, say good bye to the card."  Hank Semenec

I see: 121Ah [Unassigned]  0001h Video Multimedia

Is the card dead?

From what you say, I think you have a damaged card (bad memory or something else, but a hardware problem anyway).