Hello mr_edgeworth.
I understand you believe a graphics issue is causing your computer to freeze or produce a BSOD. I will do my best to assist you!
First, we need to determine if the issue is hardware or software-based. Please follow the steps in this document: http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en&docname=c01896793
Please respond when you complete the troubleshooting. I'm only here to help!
Mario