I no doubt think getting as hot as to not be able to touch is indicative of a fault, sounds like something is drawing too much current. (I take it this is R1/R11 on the power board?). They are series resistors in a power line, paralleled, so I'd expect some heat, but if they are getting toasty fast, and the IC1 regulator is too, i'd say something is faulty. You can narrow that part down relatively easily by disconnecting the FDD, Jack board, and Inverter connectors, and then connect one at a time, and see which one makes IC1 hot. That should identify which one is drawing too much power, and help you know where to concentrate your efforts.
Audiorepair makes a good shout too, worth checking the reset signal for the digital side of things, and if IC1 is getting hot quick, and the inverter is causing it, it could just be from the LCD being permanently blank. It may be it's highest state of draw. I do suspect you have a good grip of the bootup process, I'd go for MCU, ROM, RAM, and LCD being the basics needed. But you do have to be aware of other components pulling down the busses (Control, Data, Address) and stopping comms if something is faulty. You might be able to check this with your multimeter, measuring a digital line, if it's hard high or low, it'll read 0V or 5V, if there's comms, you should see it dance around a bit. So any data line with steady readings could be suspect. Though they would all be pretty steady if the reset signal is enforced. So check that the reset is operating correctly before you dig into the data lines n stuff.
If the reset is ok, I'd suspect chips in this order : Flash, RAM, MCU, ROM. The reason for this, is Flash does wear out, RAM is sensitive and can fail, Mask ROM tends to be quite hardy, so i'd suspect the MCU being faulty next. I take it you have done the finger test to see if any of these get hot?