This could be a result of using the wrong Transmission Fluid. You should be using ATF+4. It's a well-known issue. See this set of forum entries: http://townhall-talk.edmunds.com/WebX?14@878.0lT2aR24TD6@.ee93e7a/1332#1332
automatic transmission solenoid switch latched in low/reverse position
The 2001 Dodge Grand-Caravan has a 4-speed automatic.
The 2004 Dodge Grand-Caravan has a 4-speed automatic.
The 2005 Dodge Grand-Caravan has a 4-speed automatic.
The 2007 Dodge Grand-Caravan has a 4-speed automatic.
The 2006 Dodge Grand-Caravan has a 4-speed automatic.
The 2002 Dodge Grand-Caravan has a 4-speed automatic.
The 2010 Dodge Grand-Caravan has a 4-speed automatic.
The 2009 Dodge Grand-Caravan has a 4-speed shiftable automatic.
The 2012 Dodge Grand-Caravan has a 6-speed shiftable automatic.
The 2013 Dodge Grand-Caravan has a 6-speed shiftable automatic.
The 2014 Dodge Grand-Caravan has a 6-speed shiftable automatic.