Check the fuse block on top of the battery. In the upper right corner, there are three 30A fuses in a row. Pull the left most fuse and look at the contacts. I have fixed 3 or 4 cars where the connectors have overheated enough to melt the plastic but not blow the fuse. The fix is simple, just clean the fuse spades and sockets with a small strip of emery cloth, squeeze the sockets a bit with a pair of needle nose pliers to close them up some and reinsert the fuse. A shot of Deoxit contact cleaner wouldn't hurt either.