My system (lenny 2.6.26-2-686, P2, 2+ GHz)
The Pentium II max clockspeed was 233-450MHz .... are you sure it's not a P4? (PIII clockspeeds are 400Mhz to 1.4GHz.) So if it's a 2GHz CPu then it's got to be a P4. It helps to know what you really are running, hardware wise for us to help you diagnose a hardware problem.
Hardware freezes can happen for a few reasons, the obvious hardware issue is bad ram. If you can run memtest again, but cycle your SODIMMs out (if you have more then 1), this will help eliminate problems.
While the system is running normally, run top and watch it, see if anything spikes. In the past, I've looped a 'ps aux' and piped it to a file for review during a repeated freeze. This is the best way to see if it's a software issue. I would also install and run something like chkrootkit, rkhunter and maybe even sleuthkit and poke around for a rootkit on your laptop.
Also consider that if the laptop is as old as you say, you could have a failing piece of hardware that is forcing the CPU to divert all cycles to it for some reason (I've seen this happen in desktops, my experiences with laptops is limited to the few that I've had and worked on in the past but the general concepts would be the same. Does the laptop get hot? Not just warm (as that's normal) but outright hot to the touch.
Also, while it's frozen you say you can't select anything (with the mouse?) and you can't type. Are you able to *MOVE* the mouse?
> A: Yes.
> >Q: Are you sure?
> >>A: Because it reverses the logical flow of conversation.
> >>>Q: Why is top posting frowned upon?