Hood

Well with out much infor about the year I do the best I can. More than likely the cable broken. If your Corvette is a 74 to 82 you can open the hood by looking under the over hang of the hood. Above the wiper tray. On the right or left of hood. If you look you will see a rubber plug. It will be on firewall.
You may have to use a flash light and a mirror. But if you take a screw driver and push in the plug it will go directly to the release on the latch. Feel and push toward the front of the car. Until you hear it unlock. If needed repeat on the opposite side. If you car an 84 an up. You will not be able to open. Those years when the cable is broken. I take hours to open without cutting an hole in the hood. I have done it a few times with special tool I made. With out damage.
There is no other access.