I'm assuming you've done all the easy stuff like making sure it's plugged in, turned on, and that the plug you're using has power coming to it. If not, start there.
Then I'd check the power cord for frays or burn marks, open it up to take a look at the on/off switch, and see if the connectors are rusty. If either of the above is true, it'll need replacing.
Beyond that, check the wires to the thermostat, and the thermostat itself, looking for rust, burn marks, fraying, etc. If you find any of this, it's likely that the thermostat will need to be replaced.
handygirl, November 2008