Take your pick:
- Malware on the laptop.
- Some sort of high-bandwidth using software (e.g. media streaming, usenet client, multi-threaded ftp client) which monopolizes the Wifi LAN. (Remember Wifi is a shared medium. One bandwidth hog is all it takes. )
- Faulty Wifi adapter.
- Faulty drivers on the Wifi adaptor.
- All of the above
My best guess: Malware is the most likely cause.
To determine if it is software or hardware related: Boot from a Linux Live-CD and see if it still has the same issue.
If it does it is certainly the Wifi hardware. If not it has to be software related.
Edit: After seeing the laptop goes APIPA it almost has to be hardware or driver related. Software can't come into play as the laptop doesn't get really online. Still recommend testing with a Linux Live-CD.