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Does it stay on if you keep the Guide button pressed down?
If there is any kind of update for the controller that should be done first. The XB1 should display that if it's connected with a USB cable. Kind of sounds like there is some issue around Q8/Q9, which are responsible for turning the controller on and then keeping it on until it needs to turn itself off, but I haven't seen that on the 1914 before. Pressing Guide turns on Q8, which turns on Q9, then the controller keeps Q9 on via J3p9. Plugging it up with the USB cable kind of 'skips' all of that mess and it just stays on all the time. Could also be some other issue I've not seen before.
R7 is 0 ohms, it's just a jumper.
Q8 is probably OK if the thing is trying to turn on. Q9p1 will have around 2.8v on it when the controller is working correctly from battery power, Q9p2 and Q9p3 will measure 0v as it is turning on ground. Make sure the trace is good from J3p9 to R7, then R7 to D26, then D26 to Q9p1. Most of the schematic for that board can be fond here - https://acidmods.com/forum/index.php/topic,44711.0.html