|"it worked very well with 248MB of RAM"|
You have 256MB RAM but 8MB is being used by the onboard video. There's no way your system ever ran XP "very well" with that little RAM. Have you ever used an XP system that has 1GB RAM (or more) & a decent video card? If you have, then you know the difference. And there's no way to get your system to perform "very well" unless you add more RAM & an actual video card.
As for your restarting issue, the 1st thing you should do is disable the "automatically restart" feature. The 2nd thing you need to do is check your CPU temp. Since you said you changed the motherboard, that would mean you probably had to reinstall the CPU & heatsink. If you installed the heatsink incorrectly or didn't apply the thermal paste correctly, it will cause the CPU to heatup quickly. As the CPU gets hot, it starts to slowdown. If it gets too hot, it will shutdown. Check the temps is the BIOS.
Here's how to disable the restart feature:
And make sure you install ALL the latest available drivers.