Looking at the bomarc IIfx schematic, R4 is on sheet 1 of 8, right next to connection point C (to sheet 2), this is part of the power-switch and ADB functionality. UB16, which I think is that black box with the wire segments poking out the top, is a dual inductor that's one of the last stages of the headphone output path... and in proximity to the reset handling for some reason (why reset handling routed through the audio subsystem, or why there are two reset signals escapes me at the moment).
Still, either that trace connects to one side or the other of R4, or there's a via underneath R4. The latter should be simple to check for (it would likely be visible on the other side of the board)... but it looks like the trace from the other side of R4 heading to the left may also have rotted away.
As for R4 itself, one side connects to R23, C27, and pin 2 of UJ18, and the other side connects to the power switch, and pin 5 of UB15 (a quad inductor), and through that to C61 and pin 2 on both ADB ports. I don't know if having the power signal "stuck" or "floating" in some way can cause the symptoms that you're seeing or not.
Editing to add: Just found your images from last year. This looks like trace rot from C9 having let go (and it looks like at least one trace from R2, next to the power switch, may also be affected). But if C9 has let go then C24 probably also let go, and that's right next to the RAM slots. I'd suggest continuity-testing the traces for the RAM slot pins. They may be fine, but if they aren't then you have something that would almost certainly cause a startup failure.