When a PC runs normally for a few minutes and then crashes, especially (or exclusively) when it is engaged in compute-intensive activities like video games or playback, overheating is a prime suspect. Inspect all fans (CPU, GPU, case, power supply, any others), and blow out any accumulated dust in the machine. Monitor CPU and GPU temps while the troublesome activity is in progress; if these temps continuously rise, there is a cooling problem. The max temps for CPUs and GPUs vary with the specific chips, so you'd have to look that up.
If it's not hardware, it's usually a device driver, and usually it's a video device driver, since they contain the most complex code and the greatest number of bugs. If the BSOD is extremely troublesome, you can try updating the drivers, but keep in mind that updating drivers may correct some problems but introduce others, and the new problems may be even worse than the old. This is especially true with video drivers.
A problem with video games and playing DVDs very strongly implies either an overheating problem or a video driver bug. If it has only recently appeared in a system that has been running okay in the past, either it's overheating or something has been changed on the machine that has introduced bugs (e.g., a driver update).