From your photos, your soldering looks fine.?
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The fried transistor could be causing that continuity now.? Since you have ordered a new one, you could just remove the current one and see if the short goes away.? (It may be easier to cut the legs off first to remove the device, then un-solder the remaining parts of the legs.)
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The coil looks like it also took a lot of heat; it may be best to replace it.? You can test its continuity by probing the top of D106 and C107.? But even if it still has continuity, if there are internal wire shorts due to burned insulation, it would have a lower inductance and be less effective in filtering the power.? But it may be ok - you could also measure the inductance using the same probe points, if you have an LCR meter.
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It would be good to test D108 and see if it looks like it shorted internally, since it would also have been sinking lots of current.
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The real question, though, is "what caused this?".? I don't know.? As noted before,? it seems like one or more shorts had to be there.? I would still verify on the connector to the main board that none of the connector pins to the SMPS have any continuity to each other.? And look very carefully as you mate the control/display boards with the main board, to see if any metallic surfaces come in contact with each other.?? And next time you turn it on to test with new parts, make sure and have a 200-250mA current limit set to avoid breaking something again if there is a fault still present.
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Stan KC7XE
