* Generally, yes, the car might still run. The engine itself is usually unaffected. The transmission solenoid's job is to control fluid flow within the transmission, which is responsible for gear selection.
* However, the car likely won't shift gears properly. A stuck solenoid might prevent the transmission from shifting out of park, or it might only allow certain gears to be engaged. It could also lead to rough shifting, slipping, or complete inability to change gears.
* Some solenoids are more critical than others. A problem with a solenoid that controls a crucial function (like Park or Reverse) will be more impactful than a solenoid controlling a less critical shift.
In short, the engine might start and run, but the car's drivability will be severely compromised if a transmission solenoid is malfunctioning. It's best to get the vehicle to a mechanic to diagnose and repair the issue.
