@swampy said in Hotend won't stop heating!:

With the sd card removed and the heater unplugged both E1 and E0 lights are on (next to vin, 5v and 3.3v lights at the corner of the board)

If both are on, that suggests that the mosfet driver chip has failed. That normally happens only if the +5V rail has received excessive voltage. If you are sure that there hasn't been a short between a +5V and a +24V wire in your wiring, then I suggest you ask for your Duet to be replaced under warranty.