Quick update: On further tests, it seems that both wifi and ethernet connections are actually the same - if I connect, I get maybe 2-3 seconds before it crashes. So that's 2-3 seconds after an ethernet cable (internet access or not), or a wifi connection is established.
After upgrading my graphics card (to an ATI Radeon HD6850, see CPU-Z report), I found that my computer would BSOD right after the Welcome screen, before the desktop is shown. My initial thoughts were to enter safe mode, which I did and it booted fine. I then booted into Safe Mode...