OK, so problem was solved.
 
I think it was the simple issue of using HDMI before installing drivers. But these are the full steps (including those above) taken:
 
1. Updated the BIOS
2. Resetted CMOS
-> Due to not working, the original cards were put back in.
3. Downloaded and Installed the updates for the Intel Chipset, and the Onboard Video.
4. Went into BIOS, Turned on Multi-Monitor Support for onboard video.
5. Hooked one monitor to the VGA port of onboard video.
-> Computer booted with onboard video functioning (original cards still in PC)
6. Took out original cards, put in EVGA 1050 in the 1st 16x PCI 3.0 slot.
-> Computer booted, onboard video not functioning, this time I hooked up a monitor using a DVI cable. Video worked.
7. Installed Nvidia drivers.
8. Rebooted, hooked up second monitor via HDMI.
-> Both monitors worked.
 
Also of note: Originally, I was posting here, waiting for replies, and troubleshooting over the phone. I drove down to my brother's place today. I didn't know until then that he was using only HDMI.
But thanks for the help.