If a diode across one of the affected coils is shorted (and this is a very real possibility), it will destroy any new transistor in milliseconds - before your finger has even left the "power on" switch.
The very first, and probably MOST IMPORTANT thing to remember here is that fuses ARE NOT there to protect your equipment from damage. They are ONLY there to prevent faulty equipment from burning down your house! Fuses are mechanical devices and will not, and CAN NOT protect semiconductor devices from damage. If a fuse pops it will do so LONG after any semiconductor is destroyed.
Not throwing negative vibes here BUT not everyone is (or can ever be) an air force pilot, a dentist, candlestick maker or even ELECTRONIC TECHNICIAN.
Some things are best left to people with more knowledge in the area you need. Do you fix your own teeth?
If you wish to keep looking then do yourself a big favour and start at the beginning. I will talk about a single coil as the procedure is identical for one or 20.
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(1) Machine power off and armed with a multimeter and the knowledge to be able to use it and correctly interpret the results. Power stays OFF for this entire procedure.
(2) Cut one wire to the affected coil and check the diode across it (assuming there is a diode across the coil, AND there WILL be one somewhere even if it's on the PCB itself). You may also need to cut one end of the diode to make 100% certain it is OK or simply replace it as they are cents each (caution on the diode direction, observe the band or stripe on the cathode end).
(3) Replace the damaged or suspect transistor/MOSFET (with a suitable replacement or BETTER type) on the PCB and make 100% certain all of the connections are correct - this step is easy as you have lots of factory installed devices for comparison. Use short jumper wires to replace missing or damaged tracks (top and bottom of the PCB as required) and make 100% certain the new jumpers do not interfere with any adjacent tracks or pads.
(4) CLEAN the flux away from the damaged/newly repaired areas around the replaced parts - DO NOT SKIP THIS STEP - you might be surprised what a small amount of flux can hide from view!
(5) After repairs, using your meter again, confirm the replaced parts have similar readings ON ALL PINS to the ones around it that seem to be functioning correctly.
(6) ONLY AFTER completing all of the above steps is it 60% safe to switch the machine on, skipping any of the above is likely to end in tears.
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If you are not comfortable doing any or all of the above it might be time to ask for someone else to look at the machine possibly before much more damage is done.
It is VERY easy to cause catastrophic damage in the blink of an eye if you are not sure of what you are doing.
Good luck with it whichever way you choose to go.