(Edited to include only parts I will comment on)
When were you last home? If it was 4+ months ago, the same thing may happen at home again now.. something could have "gone wrong" since you were last home.
If the majority of the time it's shutting off is only when it's idle, let's check the simplest thing first -- Do you have power-saving enabled? (Control Panel / Power Options). (you should also check the BIOS).. Now onto the more realistic reasons for this problem...
It definitely sounds like a hardware issue. With laptops, as others have said, overheating would be the most common cause of this problem. Propping it up (make sure you don't cover any ventilation points) is an easy option. There are utilities that will check the temperature sensors -- assuming your motherboard supports it. If it is an overheating issue, there are devices you can buy specifically for this purpose.. they fit under your laptop & have several small fans. Excess dust in the motherboard & fans will definitely cause additional heat.
Anything that you know of happen with you're idle? Do you use a screen saver? Anything that runs when you're idle could be the cause. Could also be a hard drive issue. XP has an option to "Optimize Hard Disk When Idle". Try to scandisk your hard drive, then try to defrag it -- though if it is a hard disk issue, that could cause more problems, only do this once you've backed up everything that's important to you.
As for testing power, you could get a digital multimeter to see how your power is. Another option that I recommend for all computers is to use a UPS. A UPS will "condition" the power against spikes/surges/sags/etc.. It's widely believed that "bad power" causes a variety of mysterious computer problems.
Bill