My son has a 2001 Dodge Ram 1500 Laramie SLT. The check engine light will not illuminate during start up,

The ECM cost is $375 new. So that is a bit steep, it's not a lot of work to change out, the catch here is programming it. But what I would like to know is why does somebody want to change it when what you describe could be as simple as a bulb behind the light...?

...yes the main connection to chassis ground from your battery is issuing a "brown power" connection to the ECM...computers do not like varying voltage and varying amperage...take a wirebrush and clean this connection from that cable to the chassis/ground where it attaches...get steady power from a battery that is newer than five years old and in the process will have reset the Computer~....and should act normally with steady 12volts and up to 300 amps or more as needed~