2008 Chevrolet Corvette shifter moves, but gears don’t engage

My Vette recently had a dead battery, and after installing a new battery things seemed to work fine. One drive and all ok. A week later shifted to R and backed out of garage and let run in P awhile. When went to shift again, no engagement in D,R or S. Almost feels like shifter does not lock in gear selection. It moves fine to all selections, but no gear engagement. Anything common? Thank you.

First place I’d look is the linkage where it is linked at the tranny. (With engine off😏)

Suggest to start w/the standard diy’er battery/alternator voltage test. Before first start of the day the battery should measure about 12.6 volts. Immediatley after starting the engine, 13.5-15.5 volts. What do you measure?