I’m partially reviving this thread to add some detail to the above fix. I’m currently in the process of troubleshooting the exact same problem with my 2005 Quest with 177k miles.
I found that the driver’s side rear sunroof panel was leaking slightly for a long time (visible rust around the interior edge), just a drip at a time, and running down the non-visible backside of the headliner, behind and down the plastic interior trim panels, and right into the door motor and door lift transmission. This has caused the pieces to rust slightly and bind. Removing, cleaning, and re-greasing the door transmission has helped it come back to life, in combination with…
Removing the door latch motor and transmission, and also R&R-ing it with new grease. Note that I didn’t disassemble either the latch assembly or the door lift motor and transmission, but rather simply cleaned what I could see. This helped the intermittent door handle operation (just as described above), in combination with…
Replacing the rear hatch lift struts with generic bits from an online retailer. Part # 901779, $16.30 each before shipping and tax.
The hardest part of the above repairs was taking off plastic interior pieces. I did not remove the headliner fully to repair the leaking sunroof panel; instead I used clear waterproof caulk around the outside of the panel and the roof to fix that problem. (If you go this route be sure to thoroughly clean and de-grease the bonding surfaces.)
I’m probably one of the few folks who is happy with his purchase, having paid only $3500 for the van earlier in 2015. It needed a lot, but after replacing the usual suspects (engine mounts, CV axles, adjust driver’s door lock actuator arm, valve cover gaskets, and tire rotation/balance) it’s been a roomy, unique van.