The other day the car stalled going 45 mph after traveling just two blocks. It wouldn't start after I pulled to the side of the road like if it didn't have any current. I waited a minute and it started. I drove two blocks back to the house and it stalled again in the drive way. I was almost certain that the culprit was the crank positioning sensor but today I started the car in the driveway and noticed that the overdrive button on the shifter sometimes turns on the arrow on the dashboard and sometimes it doesn't. Now I am not sure if the problem is with the CPS or the overdrive solenoid. Can a faulty overdrive solenoid cause the car to stall or is that another problem that has nothing to do with the CPS and the car stalling. Any help will be appreciated.

 

Could easily be two unrelated failures. As to the OD, I'd suspect the OD relay first and then the actual wiring leading to the solenoid under the car. It gets exposed to road debris, engine oil and tranny fluid over the years. Often the insulation fails and it will intermittently ground on the chassis.
As to the dead on road business and assuming the car is the one in your sig, pull the OBD codes...that should point you in the right direction. It could be the radio suppression relay, the fuel pump relay, the crank sensor relay or the ignition module. All 4 have similar symptoms when failing.