I think it has something to do with the PCI safe scanning. It looks like I was just lucky with AIDA launching, because now it also locks up or blue screens on PCI detection most of the time. Disabling Low Level PCI detection in AIDA64 makes it launch every time, but it also won't report SPD information, so this step is somehow required.
I had only 2 cards installed: a Diamond Stealth 3D 2000 (ViRGE) and a 3Com Ethernet adapter. I've decided to replace the Diamond with another ViRGE, this time by ELSA, since I remember I've seen the Diamond in various readmes for games as causing problems sometimes. Now AIDA launches every time. Back to HWiNFO, I've disabled the Safe Search option hoping it will somehow trigger the SPD information, but no, HWiNFO still hangs on PCI detection on the ELSA. I've launched it 4 times with Safe Search and would always lock the PC.
I've removed the 3Com adapter, but it changed nothing, HWiNFO still hangs.
There's a HPT366 controller integrated on the motherboard, but I've disabled it since I don't use it. Enabling it changed nothing.
Moved the ViRGE into another slot - it changed nothing.
At this point, I'm out of ideas of what else I could change.