Paddles are tied into a circuit in the gauge cluster. If there is something wrong with the cluster it could tell the ECU thats its unsafe to shift. Most of the time that would trip limp mode.
Check all your fuses under the dash, then start looking at fuse box in engine bay. If all is good. It's a bad cluster.
Starter circuit doesn't do anything after the car is started, just stays on On Pos until you turn it off. The ECU is getting a bad signal causing it to shut off.
How do I know this; I don't. I just swapped my AT cluster for a NISMO MT cluster and experienced a few thing that surprised me. Like my paddle sifters stopped working, car kept running tho. The Park, Drive, Reverse, Neutral worked. But the point is the paddle shifter is tied into the cluster and cluster tell Engine and Trany what to do!
I hope this helped.