1996 Concorde electrical?

New battery alternator tested and good. Car will run for about 10 mins then battery light comes on. From then on the car runs like crap. backfires,gages cut in and out, radio in and out and will die if i let off the gas. Problem is that once it dies it will not start back up unless you let it cool down or jump it even though the battery reads 12v. Any suggestions. Only codes that come up is AC circuit relay.