It's fairly common in these cars. Problems arise from a variety of causes, some cheap (like the pushbutton) and others expensive (like the solenoid).

But because it went on (the light) when you hit the button and if it doesn't cancel (i.e., the light goes out) when you shut the car off and back on, it's probably just the relay. Fairly easy to fix.

Folks may tell you to open the relay and resolder it -- that's okay if you know what you're doing, but if not ...

You have to go your Volvo dealer and buy a new "overdrive relay". Then take the glove compartment out (remove screws seen around the perimeter when the door is open), and access the relays (there are two) to the left (behind the vents). Match the one with what you bought and swap them. That's it.

Good luck.