Electric train set not working - even though the light is on
The speed regulator light being on is a good start. It looks like you have things set up correctly as far as I can tell.

The first step is to identify which part is having issues. All of these parts can be purchased on Bricklink, so once you know what has failed, you can replace the defective part.

Here are some ideas for testing components:


If you have a 9V light brick or similar, you can attach it directly to the speed regulator to see if that is delivering power.
It's fairly easy to test if power is getting to the track if you have a volt meter handy. You can simply measure the voltage between the tracks when you have the regulator turned all the way up. If this reads around 9 volts, then everything is working except the train motor.
You can test the motor by connecting one pole of a 9V battery to one side of the wheels and one side of the battery to the other. You'll need to use a paper clip or something to bridge the gap. If the motor spins, you know that it isn't the issue.
You can also directly power the track using a 9V battery. You just need one pole on one rail and one on the other. You can make the connection using a small wire, paper clip, or whatever you have handy.


If any of that doesn't make sense, let me know and I can add more detail and/or pictures. Let us know what works and then we can go from there.