Your transmission is going into limp mode, It stays in what ever gear you were in when the lights came on. 60 mph means 5th gear, when you stopped and then tried to pull out, you where pulling out in 5th gear. It has happened to mine several times. I also get the brake ware indicator, brake, and asp lights, the brake lights also quit working and the fin goes up and stays up. Engine runs fine until I turn it off then no crank. Sometimes taking the battery terminals off and then back on will reset something and it will work for a while. I had more symptoms than most rcm no crank issues. I finally gave up and bought a new rcm. Instant relief, no problems since. The brake light issue is weird. If I could get the brake lights to work it would start. No lights no crank.