If you receive the "Out of video memory trying to allocate a rendering resource. Make sure your video card has the minimum required memory, and try lowering the resolution and/or closing other applications that are running." error, but your GPU has the minimum required memory, there's a chance that the GPU is having issues.
There are a few things you can do to check on this:
Verify Game Files
Always double-check that it's not a game issue by verifying the games you're seeing these errors in. Check your platform for how to do this.
Remove GPU and Recreate the Issue
Occasionally this issue will present itself as a GPU issue when it's actually a GPU issue. The best way to test this is to remove the GPU itself and run games off of the CPU's integrated graphics.
You can learn how to reseat a GPU/video card/graphics card here.
If you need further assistance, please contact our Support team.