Quoted from pete_d:

What have you done so far to try to diagnose the problem? Have you checked the outputs at the speaker, either by oscilloscope or just by swapping in a known-good speaker? Assuming the signal isn't reaching the speaker, have you done anything to work your way back to the speaker amplifier to see if/where the wires are not connected, or to see if there's simply no signal at all at the amplifier outputs?
Diagnostic steps for this will not be much different as from any other electromechanical part on the machine. Start at the part itself to make sure a) the part itself still works, and b) that it's getting the input signal it should. At least one or the other of those conditions must currently not be holding. Then if you find the problem is that the signal's not getting to the speaker, just start checking the connections at every point leading back to the origin of

What have you done so far to try to diagnose the problem? Have you checked the outputs at the speaker, either by oscilloscope or just by swapping in a known-good speaker? Assuming the signal isn't reaching the speaker, have you done anything to work your way back to the speaker amplifier to see if/where the wires are not connected, or to see if there's simply no signal at all at the amplifier outputs?
Diagnostic steps for this will not be much different as from any other electromechanical part on the machine. Start at the part itself to make sure a) the part itself still works, and b) that it's getting the input signal it should. At least one or the other of those conditions must currently not be holding. Then if you find the problem is that the signal's not getting to the speaker, just start checking the connections at every point leading back to the origin of the signal.

Quoted from pete_d:

Reseating connections is fine as a very first step. But the next step needs to be pinpointing exactly where you lose the signal.
Testing the speaker in a different machine is reasonable, but IMHO the gold standard for verifying the signal (barring using an oscilloscope) is connecting a known-good speaker to the machine that's not working. In theory, the two approaches are identical, but in practice the former only gives you a theoretical verification while the latter gives you 100% confirmation. It is unlikely, but still theoretically possible, to have a fault where the speaker works fine in a different machine, but not in the machine where you want it to work.
In any case, reseating a connection does not guarantee that a faulty connection is fixed. If you are confident that the connections are all good, feel free to skip past all that and test the output from the sound board directly to confirm your hypothesis that the problem is there. You have a good chance of being correct. But keep an open mind and be prepared to find the output from the board is fine.
If the output from the board is not fine, then you are looking at either replacing or repairing the board, depending on what your technical proficiency and comfort level is. If the board has failed in some way, it could be just about anything related to the subwoofer output, and you'll need at least a fundamental understanding of electronics and an ability to read a schematic, along with some basic testing tools (a multimeter at a minimum, preferably with at least a diode testing function, if not transistor testing function).
Note that I'm assuming the subwoofer is being driven directly from the sound board. But you said that the speakers were added aftermarket, so if you want more help you really should be very specific about what exactly is installed in this machine. In some cases people add an intermediate amp to drive aftermarket speakers, which introduces a whole new part that could have failed.

Quoted from pete_d:

I don't know that the brand of drivers (the speakers) matters. They all will work basically the same.
IMHO your next step is (as I mentioned) to verify where the signal fails. You should be able to hook known-good wires to the audio board directly and connect to the speaker, to verify that the speaker still won't work. This will rule out an issue with the wiring and narrow it to the audio board. Alligator clip wires can make this easier; but do make sure you don't accidentally short anything...often there are pin headers you're connecting to and it's easy to accidentally have a clip touching two or three pins at a time instead of just the one you wanted it to.
At that point, assuming you've verified the board is bad, it becomes a trickier thing. With an oscilloscope, it's easier, because you can just probe the board at different places until you find where the signal is actually working. I feel for the most part it doesn't take too much skill; you'd mainly be looking for a place where the voltage on the board just isn't varying at all.
But even with just a multimeter, you can do things like look for shorts (in capacitors, transistors, and diodes) or breaks (in resistors). Of course, the first thing to do is actually inspect the board; sometimes when a component fails, it leaves obvious evidence in the form of scorching on the board or, in the case of electrolytic capacitors, a swollen component, sometimes even leaking. Things that look bad, usually are bad.
To fully test most components would require removing them from the board, which becomes a labor-intensive and physically intrusive (to the board) process. I would only recommend pulling and testing components that you already have some reasonable suspicion are bad.
Whether using an oscilloscope or multimeter, you'll want to be methodical in tracing the circuit, and for that you'll want to follow the schematic. You can get that on the IPDB web site, if you don't already have it: https://www.ipdb.org/machine.cgi?id=2765
Note that based on your statement that the other speakers are working okay, I'm making the assumption that if the audio board isn't putting out the sub signal, that the problem is in the amp section and not the digital playback. I think that's a reasonable assumption, but don't have enough first-hand experience with this sort of fault nor the machine in question (Whirlwind) to say for sure.

Quoted from pete_d:

Components can fail in a variety of ways. What you're looking for is the component behaving differently than it would normally. For a resistor, that will generally mean very low resistance (less than 1 ohm), an open circuit (no continuity at all), or as you say, resistance not the same as what the resistor should be. But there are other types of components, and they have different failure modes.
You can usually measure a resistor's resistance in-circuit, but other components often can't be directly tested while they are connected to the circuit because of interactions with other components they are connected to. But even so, you can do basic continuity checking, and even diode tests (which are useful for both transistors and regular diodes) usually work okay, with some exceptions. Those kinds of tests will allow you to find components that have shorted internally, one common mode of failure (and the likely mode, if you also have overheated components on the board).
If you like, you can also take a high-resolution, in-focus photo of both sides of the board and post it here. An extra set of eyes never hurts.