Have you tried connecting the monitor to your motherboard? You do not need a dedicated GPU if you can use the on-board grpahics.
This would allow you to get into the BIOS and poke around and change settings accordingly. You could also get into Windows access the Nvidia control panel, MSI Afterburner or EVGA Precision, the Windows control panel, etc which may provide you with some answers.
Make sure you have all the correct drivers, all your PSU connections are nice and tight, and that your GPU is inserted firmly in the best PCI-E slot. If you have multiple slots then try a different one.