My bet is on the motherboard. We've had the exact same symptoms on a server in the past. I've seen hard drives cause slowness, but not to this extent. CPU is a possibility, but CPU faults are very rare in my experience. I highly doubt it's RAM, but by all means swap it out if you have some spare sticks - it would be a quick and easy fix if it is.

Anyway, +1 on the Live CD idea. I suggest removing the hard drive first. If it's still slow booting the Live CD with no drive in then you may as well put the laptop on eBay as For Parts Only and buy yourself a replacement.

If you were particularly keen to keep trying to fix it you could find a compatible CPU and try replacing that (second-hand laptop CPUs are cheap on eBay). You can get replacement motherboards as well, but unless it is an expensive laptop its unlikely to be worth the effort.