Passenger side wiper quit working

This minivan has just one wiper motor (and it obviously works), so the problem is after the motor.
The linkage between the wiper motor and the passenger wiper arm has come loose or lost a nut.
These wiper arm joints are under some fairly severe service conditions, and like to self-disassemble.

Here's the 2004 Sienna wiring diagram - enlarge to discern.

Check to see if you are even getting power to the wiper motor itself. If you are then you most likely need a new motor. 1 other thing, do you hear the motor running? if you do Dodge has this little white ring kind of thing (that's the best way I can explain it) and those are real common in breaking. If this is the case most of your auto part stores have them in stock as they are a common problem in dodges. I hope for your sake that it's the motor because getting at that white ring is a pain. You need to get to the mechanical "linkage" connecting your wiper linkage to the motor. Sorry but that's the best way I can explain it to you if this is the case. I hope thsi helped and good luck.

Sounds like your windshield wiper motor has gone bad. I would suggest buying a book for your car, testing the wiper motor and replacing as necessary. Good luck!

I suspect a bad multi function switch located in the left hand side of the steering column. This switch controls your high/low beams/wiper delay/windshield washer/turn signals and hazards.

If both wipers are not working, then first of all check your fuses, if fuses are good follow wiper motor wires or look in owner's manual to find the wiper relay. Test relay with ohmmeter to see if it is good or just replace it.
Double check all wiring.
Last possible cause would be the a bad wiper switch which you can also test with an ohmmeter

the nut that holds the arm to the wiper transmission may be loose

You will need to remove the plastic vent to access the motor. The motor should be held in by 2 or 3 bolts.

If the motor turns and wiper doesn't, that means the motor shaft is stripped and you will have to pull arm off shaft and use JB Weld and place on shaft , than replace arm and let dry for a day. OR replace motor.

the linkage in the system maybe out or the srcrew out side that retint the blade is loose

If you have already replaced the passenger side switch and it still doesnt work its a good chance that there is a pinched wire in the door itself. However usually it wont work from the drivers side either. But I still suggest looking there first.