Since you have up-to-date video drivers, do the following:
1) launch pIllusionRender manually
2) Click the "options" button
3) Uncheck "use hardware acceleration"
4) Close pIRender
Now try your render again -- it should work fine.
Ideally you don't want to turn off hardware acceleration, but it sounds like the only choice in your case. You may want to see if the video drivers you're using right now are "beta" drivers, and if they are, switch back to the latest released (non-beta) drivers.
Also, if your desktop resolution is larger than 1920 x 1080, you should be able to avoid pIRender completely by maximizing your pI3 application window so it fills your desktop.