The most likely culprit is a faulty actuator. You can test this by having someone activate the rear hatch while listening for a click or sound of some sort. If there is sound but no opening, it indicates a bad latch actuator. If there is no noise, it could be a fuse or wiring issue. You can manually unlock the door by removing the trim, but be careful around the glass latch as there are 2 push pins.
https://www.autogenius.info/chevrolet-suburban-2006-fuse-box-diagram-2/
Check the wiring in the boot that runs from the body to the top of the liftgate for broken wires.
You might have to take it to a collision shop. Remove the rear hatch panel to gain access to the latch assembly if it's not responding. If you can't get it open, take it to a collision shop as they deal with these kinds of things regularly.
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