Probably bad caps in the PSU that had nothing to do with the Voodoo1. If in doubt: test on expendable motherboard+PSU. It doesn't have to run in any sensible way (so a P4 motherboard or similar is fine), just prove whether you can boot without something blowing up.

I took the psu out.

I opened it a bit.

Looks like there is a fuse I could try to change to a new one.

I just feel worried about touching there and I don't know where I could get a replacement fuse in case the fuse is broken so I put it back together for now.

I opened it again and checked the fuse with a multimeter and fuse is fine so the problem must be somewhere else.
I did put the voodoo 1 card to another motherboard and it boots fine.
I hope the same thing won't happen if I try to install a 3dfx game and run it.

Voodoo card is working on another pc fine. I spent an hour playing tomb raider at smooth 30 fps. Too bad about the psu because it was probably the best quality psu that I had.

Do a diode check on the bridge rectifier and impedance checks on the X caps (yellow bricks in the picture above) and filter choke. I suspect something has failed open on the primary.

There's also quite a bit of dust inside that could cause all kinds of trouble so just to make sure I'd use compressed air to clean it up and examine it again.

edit: Is there any insulation (should be clear plastic film) between the bottom of the board and the case? It might be the camera, but the board looks a bit warped and some of those solder joints seem awfully close to the case which would short it.

There is some kind of insulation between the board and the case. You can see 2 layers in the picture and the layer closest to the board is some kind of foamy material.