I'm having trouble visualizing a schematic in my head... And I'm guessing the yellow wire goes to the woofer? (The inductor appears to be in series.)
Are there 4 terminals on the back for bi-amping./bi-wiring? If so, is one or both jumpers missing?
It's most-likely a bad connection but the solder connections I can see look OK. Capacitors, resistors, and inductors almost never fail, and when a resistor or inductor fails it's usually because it's literally burned-up and black.
Is that a black inductor (coil) under the red capacitor and resistor? Hopefully, it's not black because it's burned... I really wouldn't expect that to happen... And I assume the other speaker looks the same, but they could both be burned with only one completely burned-out. Does it smell burned?
A shorted coil in the tweeter section could "short out" the tweeter with little or no effect on the woofer. (And that's not good for the amplifier.)
A shorted inductor is difficult to measure because they have low DC resistance and they normally measure "almost shorted".
Otherwise,, if it is a component the red non-polarized electrolytic capacitor is the most likely suspect. If your meter doesn't have a capacitance function you can't measure capacitance, but it should measure infinite resistance after it charges-up. Either way, need to take it out of the circuit (make sure at-least one end isn't connected to anything except your meter). I'm assuming you have a soldering iron?
Or, if you remove that capacitor you can put it series with the tweeter (with nothing else) and if it's OK, it should work as a high-pass filter and the high-frequencies should be at-least as loud as with the full-crossover. If you get nothing (and the tweeter is working when directly connected, the capacitor is bad.
I assume that yellow component is a capacitor but I don't know what the markings mean and I can't tell exactly how it's wired... I'm kinda'-thinking it's in the woofer circuit.
Hopefully, at low-power.
I trust you but, sometimes you might have a bad-intermittent connection, like a small break in the voice coil or a break in the wiring to the voice coil. Then sometimes when you apply enough voltage, the voltage might "break-through" and it starts working (temporarily).