There are several things you should know / do in order to test you monitor / video card:
- Run video card benchmark. There are several programs that will do that. 3DMark for example.
3DMark Vantage is a PC benchmark suite designed to test the DirectX10 performance of your graphics card.
A 3DMark score is an overall measure of your system’s 3D gaming capabilities, based on comprehensive real-time 3D graphics and processor tests.
Note that you can test your graphic card with every 3D program (mostly, 3D mark will be more useful for that purpose)
- If you having Graphical artifacts (like the one in the picture for example):
You need to check if your graphic card don't have heating problems.
You can monitor the temperature of your graphic card (as long his got sensors)
with Riva Tuner for example.
RivaTuner is a complete powerful tweaking environment, providing you everything you may need to tune NVIDIA GPU based display adapters. The widest driver-level Direct3D / OpenGL and system tuning options, flexible profiling system allowing to make custom settings on per-application basis, both driver-level and low-level hardware access modes, unique diagnostic and real-time hardware monitoring features

- Check if the monitor is the culprit: If you got a spare monitor - plug him instead of the current one and see if the problem solved. If can't do that, make sure that all of the cables are tight and plugged correctly to the monitor / graphic card.