In all fairness, with the PS3, it is possible that the resolution is set to 'auto' which means it's dumping out a 1080p signal which the TV can't deal with properly.
Go into your video settings on the PS3 and set the output to 1080i. This is likely compatible with the TV and since most HD cable systems use 1080i as a default setting, it explains why the TV shows cable TV just fine.
It is really old stuff here, so you have to accept compatibility issues at times. But, they can be quite the headache.
If this does not work properly, hook your PS3 directly to the display, bypassing the A/V receiver. There is NOTHING about the A/V receiver which will help your image quality. PS3 out HDMI to DVI into the TV. Set the resolution as 'fixed' to 1080i on the PS3. Should work.