I mean I can... but the circuit is quite literally one single component: the volume pot. Nothing else in the power supply touches audio; the amplified audio signal literally comes straight from the game board through the harness into the pot and then out to the speakers.
With your multimeter (requirement to owning an arcade machine imo), you can test the pot easily with the resistance setting on the meter without even opening the unit. It's a 100ohm pot, so if you meter between SP+ and SP- you should get somewhere between 0 and 100 ohms. If you turn the pot, you should be able to see the value increase and decrease smoothly from roughly 0ohm to roughly 100ohm. Now if you meter between AF+ and AF- you should get the value of the pot which is 100ohm and it shouldn't change.
If the value jumps around wildly or reads very high resistance then your pot is likely bad. If one or both pairs read open circuit then likely the pot is bad or possibly there's a bad connection somewhere.
Hope this helps. It's an easy thing to look at yourself and I would encourage getting your feet wet with repairs rather than relying on sending things off.