1992 buick lesabre hood release cable broke. I can't get the hood open.

Can you remove the front grille and get at the latch mechanism?

in the car at the handle that broke you can grab the cable with visegrips or pliers and pull on the cable it should release the hood or with a long screw driver under the bumper push the release at the latch

You may need a professional to get this hood open, and it will likely need to be on a car lift. Try this if you are handy, try removing the driver side fender well liner for access to the latch.

When you say the hood release broke do you mean that you think that cable snapped? Or could it be that the latch is sticking. I had a very similar problem where I would pull on the interior hood release latch and my hood would not pop-up/spring-up to then have a lever under the hood pushed to fully life the hood to look into the engine. What I would say might be the problem is that if the cable is still intact then you might try pulling the hood release a few times to try to release the the hood so that it could spring up. Then (even if the hood does not pop up) go to the hood itself and shake it up and down. I just grab it by the grill and vigorously lift it up and down until it springs up enough to reach my hand underneath the hood to release the latch to be able to lift the hood.
Then you will want to get a can of WD-40 or some other degreaser with lubricant and apply that to the latching mechanism itself. In doing this it will break-up any foreign material on the latch and possibly the cable that would be preventing the latch from releasing. I would say you might want to apply the WD-40 on a regular basis maybe once every 3-6 months just to prevent future build-up/problems. If you have problems more frequently then of course you might want to apply the WD-40 more frequently than 3-6 months, you be the judge of this.
If this does not help then I don't have any other recommendations as I only know this to be a solution to the problem that I had that was similar. In closing, be sure to not get any of the lubricant/degreaser on belts or other parts that should not by slippery. I hope things work out for you.

if it broke at the dash,cut the cable housing down to get to the cable and pull on it with pliers,
if it broke at the latch you can still open it you will need two long skinny screwdrivers and patients

FROM UNDER THE FRONT OF THE BUMPER OR WITH A GOOD SCREW DRIVER

try reaching the hood latch mechanism thru the grille, or from under the car behind the front bumper with a long screwdriver or long pliers, or a piece of coat hanger or whatever.

Sounds like your under hood cable broke with grill off you should be able to access latch assembly and release it with a long flat bladeed screw driver.

You can access the hood release from the front of the car under and behind the front bumper.

you can reach up under the bumper and pull on the cable under there. if you need more help contact me