What do you mean by broke? Does it turn on? It looks like it's a cheap potentiometer with a built in on/off switch built into it.
I don't own one of these units, but... If the unit, doesn't come on (power up), you may want to try to open up the plastic housing. If you are good with reading the schematics, usually there are wires a red and black one for power, you could look at the circuit board see if it's labeled or test the leads with a multimeter for power.
I'd just cut the wires and solder them or wire tie them together to have the unit run 24/7 when plugged in.
Now, if it's just the POT itself, a new one could be had for pretty cheap, check out parts express.
Also, note, one could find the resistance value of the POT and put a resistor in its place. Say figure out 80% volume level, solder in a resistor, and shove it back together and use the computer to control the volume.
If you don't feel safe cutting wires one could just take it to any electronics repair shop, I think they could hack it for small charge. But, it's pretty simple.... If all else fails you could possible get a part off ebay from a nonworking system.