Your best bet is to use a DVI -> VGA adapter(most video cards come with one). to use the VGA off the video card as well.
Here lies the problem. You would also need an HDMI -> DVI cable(better then the adapter IMO).
Please note this HDMI -> DVI will limit you to 1920 x 1200 MAX screen resolution, so as long as your screen is that or lower, it will work.
If you DO want to use the onboard video, you will have to enable it in the bios. Some boards like to disable it with a dedicated card installed. This is still an option if you wish(not always a recommended option).
HDMI -> VGA NEEDS to be an active adapter as the cards HDMI port does not have any analog. You have to watch out, while you can find these hdmi -> vga cables cheap, many will not work for what you are doing.
DVI -> VGA can be passive since you have analog in the DVI slot.
HDMI -> DVI can be passive as well since HDMI is based on a single link digital DVI port + spdif audio.
Okay so just to make sure I've got this straight, my main monitor would be going from DVI to HDMI and the secondary would be VGA to DVI? So the adapters would be DVI to HDMI and VGA to DVI. Not familiar with 'passive' and 'active'.
Yes, A passive adapter means it does NOT require power or other electronics to work. It is just a cable or adapter block.
The DVI plug(or at least the one on your video card has analog and 2 links of digital.) so a simple passive(adapter the connects from the proper pins in your dvi port to the proper pins in the vga plug) will get the job done.
since you screen resolution is not too high, the HDMI ports single link connection will be perfectly fine to be for the dvi monitor. The audio portion will just be tossed away(not like it was in use anyway).
I recommend the following(images will be included )
DVI->VGA Chances are the card came with one of these HDMI -> DVI You can use an adapter instead of a cable, but I fine they are heavy with the adapter plus DVI plug and the HDMI port is just not as strong as a DVI port.
Unfortunately. The days of analog screens are getting numbered(but all screens come with a digital input now). At one point EVERY video card had at least 2 DVI ports with analog support and now even a simple GTX 650 ti card has 2 DVI ports, but only 1 will do analog VGA(with the passive adapter.)
See only the DVI port with the 4 holes around the slot(right side) on the side of the DVI port can pass analog with a passive adapter.