Electrical system has failed. Thought it was battery; it wasn't. on 1997 Chrysler LHS

Dashboard icons light up...sometimes...when turning key. Horn and power locks work...sometimes. But it won't crank, or even click. Radio, lights...all dead. Checked fuses, none blown. Relays all tight. It was working fine when I drove home for lunch yesterday. After lunch...dead as a doornail. New battery didn't help. Any ideas?

Asked by for the 1997 Chrysler LHS