Laptop crashes randomly without OS

Hi,
My so recently I decided to revamp my old t60p thinkpad.
Replaced the display, replaced the heatsink and, today replaced the HDD.

However, initially only the display seemed broken. After replacing it I could get into windows xp no problem. But I want to install slackware (linux distro) on it, so I wiped the hard drive.

When I tried setting up the partitions with GParted the computer suddenly crashed. That was the first sign that something went wrong. I tried multiple things, and it kept crashing. It crashed during the installation cd of slackware, it crashed during the HDD diagnostics in the BIOS. It crashed in the menu of universal boot cd.

After some testing it finally managed to run the HDD diagnostics test, found that a read error. so I replaced the hard drive with a brand new one. However, the same problems remain. I even thought it might be my CD drive, so I tried with a bootable USB stick, same problem: random crashes.

I tested the memory with memtest, and nothing showed up. So even though I replaced the heatsink I'm starting to think it might be heat related.

Any suggestions what I could do?

TL;DR

Laptop with no OS installed crashes randomly in: BIOS and any boot disc.
Ruled out:

- HDD (replaced with a new one)
- Memory (tested with memtest)
- CD drive (same problem with a USB liveboot)

possibilities on my list are:
- CPU
- Heat
- loose contact
- CPU
- Motherboard
- Power/battery

I'm not sure how to test all these though. And maybe this situation tells someone something more specific.