2002 qx4 sunroof will not close but not the fuse

Have you checked the fuse for the sun roof? Try this website to find the correct fuse to look at.
https://fuse-box.info/buick/buick-rendezvous-2002-2007-fuses-and-relays
You could also check the Relay. Listen to them as you or a helper pushes the button. A good relay should 'click' as you press the button.
The sunroof drain holes are hidden by the actual sunroof glass so getting to the drains is very difficult if the roof is closed.

There should be a tool that will manually close the sunroof....Remove the Fuse and consult Your Owners manual for the procedure to manually close the roof...........

The first thing you want to check is the fuses for the sunroof. Look very closely as there could be hairline fractures. If the fuses are good, you want to test the sunroof motor for power and ground. You can find testing meters here. The most likely culprit is the Sunroof Motor. I have seen this time and time again with my experience with Saturn.

Try resetting,this works on many cars
Press and hold tilt,watch sunroof untill it raises another half inch
Close tilt and test slide

Sounds like sunroof is stuck, motor can't overcome load. Cheap test: car off, interior light turned on try to move sunroof, does light dim? If yes motor is trying to move but can't. If light does not dim then motor not getting power.

did you replace the car battery just before the faults occured?
If so then with some cars the windows and sunroof needs to be programmed in the simular way to how new key fobs are programmed

check fuse
check if power at the sunroof motor
check for ground if good
if cannot close the roof apply 12v directly on motor 

The sunroof continues to open and close normally from front to back, but the vent stays open.

there is no relay in the roof assembly, just the motor. So, heck the fuse #21 on the fuse panel. Your owner manual will tell you location.

ALso, you can use a wrench, torx bit or hex wrench to close the roof in an emergency. It's on the motor. Your owner manual will tell you how to close it.

check fuse #21, 40 amp.

check switch

check motor

Good news I found out from a forum and it worked for me. Here it is

: 2002 pathfinder sunroof acts up after replacing battery (CKirbyjr) 5:30 PM 5/9/2008

Welcome to NICO -- The same thing happens whenever I disconnect my battery.
Try opening the sunroof all the way (2 inches at a time) and then close it (again two inches at a time). Turn the vehicle off and on again. Sunroof should operate normally.
I'm not sure if the last step is required but I've always done it anyway. It's worked all three times I've had my battery disconnected.