One problem related to transmission not engage has been reported for the 1999 Chevrolet Corvette. The most recently reported issues are listed below.
At approximately 20,000 miles the linkage that connected the shifter to the transmission disengaged, I do not have the service record for that service. However, I believe it was fixed under the original warranty coverage. Apparently there is a weakness in the grommet that connects the cable. On January 19, 2013, at 71,126 miles the same occurred while I was parked at a costco gas station in lake worth, florida. It required a tow to maroone Chevrolet in lake worth, florida. This service cost me $499. 34 from my personal funds. Service requires a new cable. On January 21, 2015, at 81,321 miles the problem occurred again while I was parked at the bass pro shop in palm bay, florida. This required a tow to rosner Chevrolet in melborune, florida. The service cost me $397. 55 from my personal funds. Service required a new cable and gaskets as you can see, I average about 5,000 miles per year. Albeit, this car is 16 years old and in like new condition. Having owned several cars with excess of 100,000 miles and have never experienced this problem.