Everything is powered off the 12 volt line, so that makes sense. Can you measure the 3.3v line?
DD12 is the 3.3v regulator and looks like it powers DD1, DD2, DD3, DD6 and bias for the temp sensor.
Give a good once over to all the resistors making sure the values are correct. Check the electrolytic caps, especially C37 for proper orientation. Make sure all the ICs are in the right orientation especial DD2 and DD6. If the board talks to the computer DD2 is likely OK.
1 C-37 in backwards (should not be getting hot but might hold on for a while at 3.3v if it is). **
2 DD6 in incorrectly (if so will need a new one) would cause a drain on 3.3v and not many other choices).
3 Small solder bridge on one of the fine pitch parts (solder job, normally the first guess, looks pretty good in the
photo BTW) If you used solder paste, maybe a ball stuck somewhere.
If you have a current limiting power supply, now is a good time to use it.
Just guesses from the peanut gallery.
** the only thing I know of to get a Cap hot in a circuit like this are 1) in backwards and 2) osculation, which would be hard in this case with this and the other caps in place.