You need to isolate the root of the problem. Obviously, its either the PS3, the TV, or the cables.
First thing I would do is the Video Reset, which requires putting the console in Standby and holding the power button on the console for about 5-6 seconds (wait for the second beep). This will revert the Display Settings to display video via the A/V cables that came with the PS3. Right now, I would forget about HDMI for two reasons:
1. HDMI video is not as bulletproof/reliable as RCA video is.
2. Considering the first reason, IMO, the RCA not working is a bigger problem than the HDMI not working.
If the A/V cables don't display anything on the Panasonic, try using them on another TV. Remember to choose the proper input channel on each TV. Also, try to "jiggle" the RCA video connection on both TVs if video doesn't immediately shows up. These connections can sometimes come loose overtime as the TV ages or is moved around a lot and can cause a loss of video from the connected device (this happens with one of the A/V inputs on my friend's big screen TV). All of this should help you figure out whether or not the TV is really the problem.
If you cannot get RCA to go on either TV, try the HDMI. The PS3 should automatically detect it and take you through the Display Setup for the HDMI, so there is no real point in doing the Video Reset described above. Again, make sure you are on the right input channel on your TV.
If that still doesn't work, I would try using different cables or using the current cables on another PS3. This will help determine if the PS3 or cables are at fault.
Its worth noting that the PS3 requires HDCP compatibility in order to display video via HDMI, but this is usually an issue with older HD computer monitors, not so much HDTVs.
Also make sure that the connections are clean & free of dust/debris and are not damaged.
Good luck.
