Windshield wipers wont turn off and the turn signals wont turn on in a 2010 Dodge Journey

My wife has had issues with locking her doors (they would unlock but not lock [neither the fob or the interior button worked]) for about 6 months. Now she tried to start her 08 Nitro but it would not start (dash lights still worked but nothing else). So naturally we think it is the battery. Take...