GFCI outlet won't come on
Not an uncommon problem. I have had a lot of problems with GFI's the last few years myself. There are a few likely causes:


A fault still exists and will not allow the GFI to reset.
The GFI tripped due to an overload and the differential circuit was damaged, thus the outlet is now toast.  This seems to be a common complaint with standard 15 amp GFIC's. they don't take current spikes well.  In your case 1500 watts on 120VAC is pulling around 12.5 amps, which is getting close to max capacity. Sometimes the initial current draw is much higher as the resistive load needs to heat up a bit before  it reaches its operating impedance. A "cold" load can offer a much lower impedence and cause a short duration, but large spike of current to flow at turn on. Very common on motor loads, but not uncommon with filament heating or lighting.
Sometimes if you turn off the power to this GFI at the breaker, then push the test and reset buttons, then turn the power back on again, the GFI will default to the tripped condition, but will reset. 
Disconnect any wires connected to the "Load" side of the GFI. Unplug all loads from the GFI itself, and give it a try.
If none of the above items work for you, you will probably need to replace the GFI. Find one with a 20 amp rating instead of 15 amps, assuming that 15 amp is what you have now.