Yeah, I'd be leaning towards power supply but that particular card only requires a 400 watt PSU, It is possible you are still underwatted if this was a dell or an HP computer you are upgrading, but thats not necessarily the most likely scenario in this case given how little wattage that card draws. I'd check and see if you got a cable lodged in the video card fan itself when you installed it, no fan at idle would tend to overheat the card after around 30 minutes even with large case fans. Also check the CPU fan, etc. If its not that, it could be driver related. Check intel.com for a driver update for that integrated intel card. Even if you aren't using it, it's still present in the system resources and could be conflicting. I'd check the same thing for the other drivers while you are at it.
The next step if that doesn't do the trick, will be to check event viewer (controll panel, administrative tools, event viewer) under system and application to see if there are any crashes or errors reported before the machine crashes in the logs. Also download and check bluescreenview and see if there are any hardware related BSOD's http://www.nirsoft.net/utils/blue_screen_view.html
The other possibility of what is going on here, is you may be hitting the ram limits of a 32 bit operating system. If you have the 1GB ram variant of the 5450, and you have 4GB ram inside your computer, your computer can't access and address all of its ram, and those addresses include the video card ram pool to a certain degree. Windows XP alone can only utilize 3.3GB worth of system ram. With a video card under 512MB, the amount of used ram addresses doesn't really detract from that 3.3GB pool. When you exceed 512MB though, the card memory starts requireing the same addresses that the system memory needs, so you can end up with only 2.5-2.8GB usable system ram. Couple that with a few running programs in the background, whatever the Intel video card has locked up and used, etc, and you could literally just be running out of available ram. Check task Manager and see if your ram and CPU utilization is constantly up pretty high.
Either way, you really should get a new computer. A pentium D is technically dual core, but they are sloooooowwwwwwww. Even a core 2 processor is at a minimum twice as fast. Going with a minimal cost overall upgrade would dramatically speed up your computer and allow you to use more than 4GB ram. You may not be able to use windows 7 with that particular computer by the way, thats one of the motherboards that need a bios update (if they made one) for the windows 7 genuine advantage licensing module to function correctly, same with the P5lD2