My 2005 Dodge Grand Caravan fuel gauge does not move. I have gas in the tank, but the gauge shows the tank is empty (in fact, the dial is ~ 1/4" below "E").

The sender unit in the tank has probably failed and needs replacing.

Sounds like a bad connection at the gas tank harness.

Sounds like your sending unit could be bad.

Could be a problem with the gauge in the instrument cluster, or the wiring that goes back to the tank, or the sending unit in the tank.
The sending unit has a float much like your toilet which could stick or fail to move.

it's in the wiring of the sending unit check for a bad ground or broke wire

worth checking the fuel tank for holes or there might be some fuel delivery pipes leaking badly. Or it might be an O2 sensor not giving correct signal to ecu thus consuming so much fuel.

The float sending unit is messed up and don't know now much gas is in the tank. The float may be stuck in a higher position showing more gas, in reality the gas level is way below. Try using a rubber mallet and tap on the gas tank near the fuel pump. It may help free up the float.

MAYBE THE PROBLEM IS IN THE TANK PROBABLY THE CIRCUIT ATTACHED TO THE FUEL PUMP THE ONE READ THE FUEL IN THE TANCK IS GOING BAD

check the grounds on your fuel tank sending unit,must drop the tank to do this. with the tank down,remove the ground and look at your fuel gauge it should read full or empty,if it does not it may be a sending unit

They could have installed the wrong pump assembly. I would first check to see if the float arm is binding on something not allowing it to reach the empty position. If you take the assembly out, have the key onand work the sender up and down thru its travel and see if the gauge matches the sender position. Disconnect the wire going to the pump so it doesn't get damaged.