How do I adjust the hood latch release cable on my 2002 Pontiac Bonneville

Heidi, No electric release. The latch is probably stuck. While you pull the interior hood release have an assistant push down and pull up repeatably/vigorously until hood releases from stuck position. Lube latch and cable before closing hood. Check the attached links,instruction and guides, Good luck
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...when the cable has broken to the hood latch. I am assuming this is what you mean. If working the hood release from inside the car doesn't do the trick then you are going to have to try and pop the release from outside at the front of the car. You're gonna have to fire up your ingenuity and figure it out 'cause how you do this is different for every car out there. A quick search came up with this:

http://www.pontiacbonnevilleclub.com/forum/1987/topic26052.html

Do some internet sleuthing; you'll find lots of suggestions.

Try using a screw driver to reach the hood release under the hood. You may need to pry the hood up a little to reach it. The electronic release is there as a secondary latch for safety. You can still open it up if you can get to the manual release.

The hood cable is not adjustable, you must have a defective cable or the latch is sticking under the hood.

There are adjustment screws in the center of the rubber bumpers that adjust hood height. Try letting the hood down a little by turning the screws clockwise

If the cable isn't broken, have someone push down on the hood when the release is pulled, it should release. If it does, you should apply some lube to the latch mechinism to keep it freely working. If the cable is broken, you reach in behind the grille with a small hooked tool and find the cable going to the latch, hook the cable and pull it out 'this will take quite a bit of force' so you can grab it, you then remove the plastic housing and grab the steel cable with a pliers or other tool and from the latch side- pull hard to release the latch. you should then will have to replace the cable later. Also lube the latch.

sometimes the hood adjustment for the latch is too tight, pull the hood latch, go out to the hood and press down on it at the latch location, push hard and release quickly, then adjust the latch before closing hood

Have someone stand on the outside of the car and lighty tap at the front of the hood right in the middle as you pull handle out and if it doesn't open repeat a few times if you get it open oil the latch iwth like wd 40 or even better pb blaster if you can get it.

Some cars have a picture of it under the hood near the latch.

See if you can grab the broken cable end with a pair of vise grips then just pull. It also helps to give a slight bounce on the leading edge of the hood while pulling, to take tension off the lock mechanism if it is binding.
The cable is exactly like the hand brake cable on a bicycle...You need to pull the inner cable.