20 Most Recent 2013 Dodge Avenger - Page 5 Questions & Answers

check the dashboard dimmer control, either part of or next to the headlight switch, sometimes the contact on the rheostat goes bad or the contact at the connector plug

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Some anti-theft systems need to be reset after the battery has died and/or been replaced. Check your driver's handbook for more information on this.

Had a SIMILAR problem, turned out to be a loose connection on the alternator wires and a poor earth. Maybe worth having the battery tested too