My oldish lappy tries to load XP but suddenly switches itself off. I think its a hardware fault. I used to have an old floppy with test software on it in the olden days which would run basic tests on the various hardware components in computers. Talking of 15 years ago. Anyone know of similar software available today?

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You can eliminate a software problem by burning a Linux boot CD and trying to boot from that, but i am pretty sure it is hardware.
I have seen this type of fault a few times usually on Sony or Acer either the motherboard or the separate power board.
Usually not worth fixing, but if you do a search on your particular make & model it will usually turn up a known fault.

Try Memtest86. You burn it to a CD then run it when you boot and it will test the RAM for any problems. Run it for a couple of hours.