What would cause ABS and brake lights to stay on after battery went bad and

Check ALL fuses first!! See owners manual for fuse location and function. Then if no luck, get the ABS scanned for codes. First thing to do with any elect. problem is check the fuses!!!

Most likely you'll have codes stored for low voltage and communication issues. This will be because the battery went dead. As Pushrod said, have scanned for codes, and have them cleared.