You don't get power to your woofer unless the speaker is getting driving voltage/current.
Your meter can check AC or DC voltage. You have to select the proper voltage type when testing.
Your transformer is probably working alright.
There really aren't that many components in these speaker driving circuits.
Unless you can see actual physical damage to components (burned or destroyed parts), you have either
capacitor or semiconductor damage. (or a blown speaker itself)
Do you see any actual physical damage to any of the electronic components?
As I said, my usual suspects with my kid's speakers was semiconductor damage. Transistors or diodes.
Resistors rarely get damaged unless you can actually see burned transistors.
Frankly, you can probably replace every capacitor and semiconductor in those things for not very much
money to get it working again if you lack the skills to troubleshoot to component level.
If I were you, I'd suspect the transistors, knowing the experiences I had.
