The code that comes up on my 05 vibe is something about a relay or a ground.

Hello, What is the actual code that the vehicle gives you? It will be 5 digits, beginning with a letter followed by 4 numbers. Also, when it was jump started, did you notice sparks flying anywhere? Was the battery ever connected incorrectly? Did the large wire on the alternator spark when removed, or spark when touching other components? My concern is centered around shorting battery power to the chassis, and that may be the cause of your issue. Typical when a battery is jumped or service.