I would go to a wrecking yard and look at the same type of vehicle and fashion a homemade tool device to jimmy the hood open,. The latch is located in front of the radaiator, I would look around the neighborhood for another GM car of that vintage to familiarize myself... .
I've got a '93 Cutlass Supreme, and judging by the body style I don't imagine much has changed. I was able to get my hood open by hand, no tool required. In between the radiator and the front bumper is a space that will allow you to access the latch. All that you can see from this angle is the spring that secures the latch when you close the hood, but you can feel the mechanism. If you push back the plastic that backs the bumper, you can even see the wire (in its plastic casing) that releases the hood.
By laying on the ground (feet toward the passenger side of the car), I was able to pull the latch open. The latch is spring loaded as well. It swings on a point near the hood itself. In order to release the latch, look for the end of the wire that pulls open the latch. If it's clean it will be bright aluminum. Unfortunately, the reason that it is probably stuck is that it is all gummed up with dirt and grime. You should be able to follow along the wire as I mentioned before and feel the end cap. Pull the lever that the wire is attached to toward the driver's side of the car. It may take some doing, but it should release the latch.
I haven't resolved the problem yet, but at least you can get the hood open. I know that a couple of years ago, my latch started to stick. I doused it with WD-40 and when it dried I coated it in white lithium grease. Unfortunately I think this only compounded the problem by providing a sticky surface for grime to build upon, which resulted in the latch getting too jammed to open by the regular method. I have cleaned it again with WD-40 and it appears to be OK. I will post more once I am sure I have actually got it in working order.
I too had this problem with my 92, if most everything is still intact. After you've done the things mentioned above by these helpful dudes. You may have jiggled it enough around (played with the inner mechanisms). You may try standing on the broke cable inside the car and with pliers er, whatever pull it again and then go try to lift the hood. Mine came open like that. Car had been giving me fits. So, i actually broke the inside lever twice. 1st one pulled the plastic piece off. second one broke the end of the wire, and tore it off the floor. Anger never helps, hah. Think things through is good advice.