You might going to be in trouble mining with 2x 512Mb DDR2 ram .
Are you using a TV as a monitor ? Are you sure the TV supporting the Screen resolution / Frequency what is the output of your vga cards ?
"How do I start troubleshooting this?"
Try connecting to a computer monitor . Did you installed any driver for your cards ? or just plugged in the card and connected to the TV ?
Edit:
After a while I got this garbage on screen:
That garbage on the tv screen might mean your tv can not handle the signal from your vga card . Im building computers for years , built a lot of HTPC for special requests. This happened with me a few times in the beginning when i tried to set up the HTPC with a tv . After i connected a monitor , installed the right drivers , and then connected the HTPC to the the TV , problem always resolved .