The 330 series don't have an on button (they are on all the time, unless you unplug them), so presumably you are saying it is plugged in but the light is not on, the button on the front doesn't respond, and it doesn't print.
I'll assume that you have checked that the power supply is plugged in to a known working power socket and the socket is switched on if applicable (depends on country), and that you have checked the power cable is firmly plugged into the labelwriter.
Check to see if the power supply has an LED on it. If it has but it is NOT lit, and is definately plugged in then it is probably a dead power supply (or possibly a blown fuse).
In this case you can try a replacement power supply:
Dymo LabelWriters (2nd item from bottom)
If the LED is lit then it would suggest that the labelwriter is broken.