What would cause the transmission not to engage in any gear in a 2004 Town & Country Touring 3.8 6 cyclinder that will not engage in any gear.

Take several things into consideration. The car sounds like it needs a transmission. If it has, say, 150,000 miles on the original engine, bald tires, a big dent and/or rust, trashed interior, headliner falling seats ripped up, all that, forget it and get what you can from a junkyard, it's 19 years old. Now let's say it has 50,000 miles, good body, and paint, all the glass good, tires and brakes good, then consider spending money for that trannny