As you are aware, the convertible top deck latches catch on the serrated pins (latch pins) attached to the convertible top rear bow. Once you have the top released from the deck, I would try pushing the top down onto the deck to the first serration to see if it releases from that position. If it does, then push the top down to the second serration and repeat the procedure until you have done this with all the serrations. You should also lubricate the latches and then observe the mechanism when pulling the latch release handle to determine if the latches travel back to the full release point. If not, then one must either adjust the latches, the release cable (should not have any play in the cable), the latch pins, or purchase new mechanisms. I would suspect that if the latches work properly when you test them, new ones are not needed, just an adjustment is required.
On the C4s, the removable hard top has latch pins or bolts that fit into the latches, but do not hold the hard top down securely unless the bolts are tighened with a wrench. On my 91 and 94 convertibles, the hard top would not always release the pins or bolts from the latches when I wanted to remove it. I would loosen the windshield bolts and jiggle the top a little after removing the bolts from the B pillars (convertible top does not have B pillar bolts). You might want to try moving the top up from the windshield a little to see if the rear latch pins release. The factory service manual (FSM) states that to release the convertible top from the deck, first release the windshield latches and lightly push up on the front bow at the windshield, then pull the deck release handle and push up on the Number 5 bow (the one at the rear of the top that sits on the deck). The latch pins should release from the deck latches. It was always my fear that the latches would not release and that I would have to crawl under the deck to release the pins. Therefore I always examined the latch mechanism and cables for proper operation when I dropped the top. If the cable moved the locking mechanism cleanly from the latch pin hole, then I was sure that the top would release from the deck. I always examined the cables for wear and fraying.
Since you just purhased the corvette, I recommend that you purchase a FSM for the 1993. They become available on e-bay or the forums, or you can purchase a new ones (two volume set). Get the red ones.
I hope this helps, and enjoy your corvette. In my opinion, driving with the top down is the ultimate way to cruise in the car.
Barrett