One of the easiest ways to stress test a graphics card is to use the Really Slick Screensavers. These are a set of screensavers that I discovered in high school during my early days of running RedHat/Fedora Linux. Most of the screensavers can be tuned to fully utilize the hardware (particularly the lattice screensaver) and may help to implicate the graphics card as a failing component. The last time I visited the site, there was both an installer and a zip file containing the screensavers. Once the screen savers are installed, they can be configured and testing can begin.
Looking at the settings for the lattice screensaver,
The computational complexity and the stress applied to the hardware can be increased by increasing parameters such as the latitudinal and longitudinal divisions of the tori as well as the depth and density. Not all shutdowns indicate hardware failure, they may also indicate other issues such as a failing/underpowered power supply and overheating.
Windows Crash Dump Analysis
Identifying Cooling Issues
Troubleshooting Memory Errors
Stress Testing a CPU to Detect Hardware Failure
How to Detect a Failing Hard Drive