Here ya go...a cct diagram..from what my beady eyes can see.
This is a standard PWM heater design.
Obviously the 555 is dead. This is usually caused by overvoltage. D3 looks like a zener lets say 16Volts Zener. D1/D2 are IN4148's or equivalent.
The FET may have shorted gate to source (or drain). Take it out & replace the 555 & power up. If Ok it may be the FET. A replacement FET would be IRF540N from Jaycar.
Hope this helps.
edit:
opps the LED is connected to R1...I just drew it as a diode
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