Which P4? my workshop/basement PC has the 541, bit newer but it's still ancient to run W7 on it, Vista wasn't even considered as it's basically a beta OS that was released on a rush.
I run 2K on it as XP crashes the same way as yours, tries to load but restarts, probably a driver conflict of sorts even though the motherboard is XP compatible, I used it to play the test build of Half-Life yesterday but its main use is working with floppy disks.

Only works offline though, no networking.

Mine was made in 2003. The blue screen it gives stays there and I can't press any keys and the HDD stops.

HDD suddenly stopping in fact may be a hardware problem, dry capacitor(s) at power supply outputs causing +5V/+12V rails going out of spec, or having high ripple.