Sounds like a THERMAL SHUTDOWN to me...
when burning DVD's and CD's, there is a heck of alot of heat produced, this needs to go somewhere... if the ventilation is bad within the PC, and the Thermal Thresholds settings in the BIOS are low, then PC will shut down, in order to safe itself...
to check this avenue, open up the PC, have a DESK fan blow onto the general area of the MoBo, then try to burn a DVD/CD if it does not shut down, then that was the case...
also check your TEMP settings in the BIOS...
Ben
"If it works don't fix it! If it doesn't use a sledgehammer..."