I have a 1991 Silverado, and I had this same problem some years back. This going to sound silly, but put the vehicle in neutral and try gently rocking it forward and backward a bit. This let mine go once when I first had this problem.
Bottom line is, the ignition is going bad and you need to replace it. I replaced mine, and it has worked fine ever since. Only thing is I miss having the matching door and ignition keys. Dunno if yours just has the one key or not, but mine has separate keys. I guess if you have to replace the ignition too, you'll soon have two keys too weither you did before or not!
Replace it as soon as possible, because even if it unsticks, and works for a while, it IS going to happen again and get worse too. Take this advice from the voice of experience.