Samsung HDTV's are anything but sucky. Samsung is the leader now after beating Sony a few years ago. They are pretty much universally praised. This is not the same company we all hated who used to make horrible tube SDTVs back in the day. They went from bargain crap to cutting edge pretty darn quickly.
In any effect I have tested over 20 HDTV's in home as they came to the market. (was very picky and wanted to REALLY see what was what) I now have a 52 inch Samsung LCD and 50 inch Samsung DLP. Both take composite video with absolutely no problem. (120hz and 60hz) I don't see how the refresh rate will affect anything. The SNES is a 60hz device and Samsung's plasma line accepts both 60hz and 72hz native. The Plasma will do all the conversions it's self. I don't think it's even possible for it to try and ask more of the console making it overheat. Overheating is most likely due to your power adapter about to die. Mine heated up and practically burned out.
I've never seen a composite/component hybrid connection but as another poster said, it's 90% likely you just need to toggle between the two modes in the menu. I don't think analog sources can auto detect. The "weak signal" error pretty much confirms it. Your friend just needs to use an S-Video cable and be done with it.
If you can give me the model number of the TV I'd be happy to try and help. HDTV's play 2D games soooooo nice. Old 3D not so much.