I've been designing and building circuits and working with microcontroller and PI type devices for over 30 years. I once built a custom designed wire-wrap board for a 286 computer complete with video capture, ultrasonic capture, audio, IR, motor controllers and all with over 3000 wire-wrap connections - so I have a little experience with this type of troubleshooting.
Now, I don't have any schematics for our R2's, but if you're getting a lurch forward and a solid red light but nothing else - then here's my diagnosis (for what it's worth):
The MCU, the head motor cable or the head motor itself is bad. I'm sure that the startup routine is frozen trying to rotate the head waiting for one of the head rotation limit sensors to fire. There probably isn't a timeout in the routine, so it is going to wait forever for the limit detector to change states, which will never happen since the head isn't moving. With the lurch and the light that is a pretty good indicator that the PI is working, that the MCU is at least partially working and that the cable between the PI and the MCU is good.
Looking at the most obvious - a mechanical problem - is the head motor turning/making a noise, but the head not moving? I'm guessing not since you didn't mention hearing a sound.
So that would indicate an electrical or electronic issue. In cases like this, cabling is almost always the culprit. It is possible that a whole batch of MCU's were manufactured with a singlar defect, but I'm sure this was outsourced to a company that employed robotics to assemble the board and decent QA controls that would reduce the likelihood of systemic errors like this (the boards themselves look to be of decent manufacturing quality). Motors, the same deal - really rare for a motor like this to fail right out of the box.
I don't know if you have access to a multimeter, but if you do - check continuity between the pins on the MCU and the corresponding pins on the head motor with the cable connected. If you look at the board on the side opposite of the cable connector you'll see the solder pads. Just check that you get a beep on each of the 6 matching pads and that will eliminate the cable as the problem.
If your cable continuity is good, or if you don't have a multimeter - try swapping the connector for the head motor with one of the leg motors. The connectors are the same. Lift R2's head off the spindle. Start it up. If the head motor jerks a bit, then that means that the head cable and motor is good and that the MCU must be the problem. If the head motor doesn't jerk - then it is the cable, the motor or your R2 head is seized up - most likely the cable is bad. If you've plugged the leg wires into the head connector - your R2 will probably begin turning in circles, so be ready for that. If it does, then that is a solid indicator that the MCU is not the problem at all.
It is pretty easy to force a cable in backwards, bend a pin, or fail to seat a header properly. Sometimes, too, a pin can break free from the solder (particularly since we are all inserting and removing headers repeatedly), so the pin itself is there, but not actually contacting the trace on the board.
Good luck!
Current Builds: R2D2, Millenium Falcon