What application is being used for videos?
I would try VLC found at videolan.org and see if it runs fine or not, it's advantage is built in codecs and free, and pretty well regarded.
This will help rule out the application being used since you said the 2nd monitor still functions and doesn't go ART screen on ya at same time.
You monitoring your video card temps?
If spiking high for the range of that card, check fan(s) or paste.
Download GPU-Z from cpuid.com and snag CPU-Z too to check CPU temps.
You overclocked on that video card at all?
Check voltage on it as well, if out of range of normal, card might be failing.