My goodness, I think I've found the answer! Well,
an answer.
I was having the same problem. My system kept locking up when doing things such as Flash, YouTube, ReaPlayer. I combed forums and made a huge list of what it could be. It would either lock up or reboot.
I have an Athlon XP 2100+ with 1 gig of RAM on a Gigabyte GA-7ZXE running XpPro (no Service Pack).
Making a long story short, I kept racking my brain to think of the commonalities of these tasks. Then it hit me - CPU activity. Was my CPU getting too hot?
I downloaded Motherboard Monitor and it seemed that it would lock up or reboot when hitting 74 degrees C. Without doing anything, it was hovering around 71 (roughly 160 degrees F). My CPU would get hotter when performing the aforementioned activities.
My CPU fan was functioning but it was very dusty and, silly me, I never used any thermal paste.
I went out and bought a Vantec Aeroflow 2 (VA4-7245) that came with thermal paste. I applied the paste and new fan/heatsink combo, booted up my system, and the temp was now down to ***36 C***
Running YouTube or RealPlayer would bring it up to 45 but nowhere near the danger zone. I've running videos and RealPlayer for the past half hour with no problems!
So, check your CPU temp!!!!