Remote makes the car beep, but not releasing the trunk, has the cooler in rear seat center back, seen people say their key wasn't opening it, I don't see a key place on the trunk area ?

 

What if you push the button on the trunk lid itself? Does that open it? If that works I suspect you need a new, decent quality battery for the fob.
The key slot is towards the left side under the lip, nowhere near the trunk lid button.

If the physical key doesn't work then you probably have a Valet key which does not give access to the trunk.
If you have another key, try with that. Otherwise you'll need to get a Master key.

 

Keep in mind, the 2002s won't have a button to open the trunk from the outside, as they do not have the proximity key. The lock cylinder will be under the chrome part of the trunk where the license plate lamps are, in a weird position, facing towards the ground. You basically have to come up from underneath with the key blade facing up towards the sky.

Does the interior trunk release switch work?

 

Key works the trunk key switch by gas door opener inside, but doesn't turn in the slot on the trunk itself, remote doesn't work as well as the pull by gas release doesn't work, was my sister's car, she passed away so we are trying to figure out what to do with it

 

Squirt some graphite up the keyhole and bang on top of trunk with bottom side of fist while you are trying to turn the key. You just need to unfreeze the mechanism and a lot of times that will work. Once open lube mechanism good with white grease. If key won't turn after this try banging on top of trunk while someone inside keeps pushing the trunk button.

 

Does it turn clockwise or counter clockwise ?

 

It turns Clockwise

 

I pulled my rear trunk lock cylinder out out since I'm not able to turn the key since it's full of crud. Has anyone ever replaced this cylinder or have a locksmith work on it?

 

If you have the cylinder out why not just clean out the lock cylinder?
I use spray Isopropyl Alcohol to hose out the cylinder until no more crud comes out.
Then spray with a good quality penetrating oil (not WD40 or graphite lock spray).
Then work the cylinder by putting the key in/out and turning it a few times.
If the problem is with the linkages you will need to fix that as well.

Otherwise take the cylinder to an Automotive lock specialist.