OK, there's a possibility that you have a motherboard problem but before spending a load of money, can you check the hot end thermistor? I don't have the same printer as you (I have a GeeeTech Prusa i3 Pro
where I had problems with the hot bed. The temperature on switch on should display the ambient temperature of both the hot end and the hot bed plus the default temperatures you've set when heated up
Example: Hot End 17/200 Hot Bed: 17/65
Pictures of the Tevo look like the display is common to most i3 printers. What does your printer display on power up?
Disconnect the hot end thermistor at the motherboard (With the power off!) and power up again, the hot end should say 0/200 or equivalent. Can you use a continuity meter (Multimeter on Ohms setting) and measure the resistance of the thermistor when disconnected, I think it should be something like 130Kohms?
My problem was due to a broken wire in the cable to the printhead so I got a disconnected 0/65 display. The hot end works the same way as the bed. I reckon if the thermistor or cabling is shorted out it'll force the heater to stay on as it's unable to regulate.
You said you'd changed the extruder, did this include the thermistor or was it just the extruder and heater assembly? If you changed the heater AND associated thermistor then the board may be the next thing to investigate.
Play Bonny!
Soadyheid