Couple of things here.....
DVI outputs vary a bit....there is DVI digital, DVI analog, and DVI that output both types of signals.
Your video card probably either outputs the combined analog/digital signal or digital only. Check the specs on your video card.
If it outputs digital only, you'll need a converter box (which are very spendy) to do the conversion prior to connection to the analog component jacks on your TV.
If your video card does output an analog signal over the DVI, you may have to set the resolution very low so that the TV can sync the signal.
I tried for a couple of years to connect a PC to two different TV's for my mame cab. I tried cards with TV-out options, going through RF modulators, etc. I was never happy with the results (and the TV's weren't very pleased either!) so I settled for a PC monitor that I had sitting around.
Good Luck!