Hi, Dave,
Firstly, could the actual flipper and its round metal shaft be wrongly positioned (or even slightly loose) in the 'crank' which clamps around the shaft? Or does the flipper drop to the 'proper' alignment without the power on? If it does, then this sounds like a problem with the coil drives.
With the door open, the power interlock should cut off the solenoid & flashbulb power, so assuming this open the door and press the 'Enter' button. I expect there'll be a 'Test Report' announced, quite possibly for 'End of Stroke Left Flipper, Switch F#'. That's the switch you mention, operated (pushed closed) by the flipper linkage. Don't worry about that for now, it doesn't (or shouldn't) have a direct link to the flipper coil.
After the report has finished, use + or - button followed by Enter to select 'Test Menu', then repeat to select 'Switch Edges'. Now press the left flipper button, there should be an indication of 'Left Flipper, F#' with the button pushed in a little, followed by 'Upper Left Flipper(s), F#' with the button pushed right in. If you see this, then the little circuit board attached to the flipper button is working, and being read properly by the 'Fliptronic II' and Cpu boards. Then push in each of the two switches which are operated by a metal bracket on the back of the door. One should show 'Coin Door Closed, Switch 2#', the other is the power interlock. With this pushed in, the flipper power circuits are active, i.e. when in the test routines the flipper buttons will operate the flippers. If the left flipper now moves to the raised position without the button pressed, then it is a coil drive problem. Let go of the interlock again.
As ronsplooter says, the power winding of a flipper coil will burn out very quickly if it's 'locked on', so this one could be the lower-rated 'hold' winding of the coil being energised when not needed. When power is first applied, does the flipper raise slowly? In this type of flipper, the hold winding contributes to the normal movement of the flipper (not by much, but it does).
I gather you've recently acquired and moved the machine. It may help to re-check any connectors disturbed during the move, as well as the grey 'ribbon' cables between circuit boards.