Starting issue

  mercedes/e-class/1996-2003

I have a 1997 Mercedes e320 that had a bad battery. Changed the battery car worked ok for a while then it sat and wouldn't start unless jumped. Then wouldn't accelerate and ran rough so I did all resets with ignition switch, jumped it and once started it runs fine. But as soon as I shut it off, it won't restart. There is absolutely no sound when I turn the key. Put jumper back on, it starts fine. What else can I try before I have to take it to a high priced dealer?

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