i think that proximal end of the power resistor was connected to a trace which went diagonally over to the the input of the voltage regulator and that the second resistor connected across from the input to the output of the voltage regulator. but you have 3 voltage regulators in TO220 packages in a row, so not sure which is for 12V and which is for the 5V. it may be that when you filled in the void with solder, you ended up shorting out 2 traces which were close initially, but not connected. so when you filled the hole with solder, it ended up having a different circuit configuration, and the little bit of current leaking through the burned up power resistor is just enough to allow the logic and drivers to run, but gives you problems. it would be neat if there was someone who has a picture of that pcb and could post it up so we could compare, then have some idea of how to fix it.
if it is not supposed to be connected and you put a new power resistor in there, could be problems again. the proximal end where it burned the hole in the board doesn't actually have to go to the board, you could find a replacement resistor and connect it from the Vcc on the distal end all the way over directly to the input to the voltage regulator i suspect, then figure out what to do about the solder blob you put back.
you can go read the infineon transistor modification thread that geoff started following knuckles design for the 'any voltage' power resistor replacement. that was the only thing i had to go on until i looked in mine and saw how it worked. mine is the 9FET infineon, but is pretty much the same on all controllers i think.
maybe more closeups in there so we can see where the traces run underneath those 2 resistors and what the TO220 packages are would be a start.
if you can get the voltage regulators working again, and have a new controller to depend on, then you could use this one to hop up the shunt and swap out the FETS for more power. then if you blow this one up again , you would still have a working, if normal, controller.