@AAH may be best to advise here as well. I would perhaps send him a private message, or use his contact-us link on his website if you can not get hold of him here, he makes the boards so will be best to advise further.
There may have been a short on the board which took out the reverse polarity...
That sounds like the diode is shorted so it's conducting in both directions. Was your wiring reversed at any stage? The diode should not fail under normal use.
What do you mean by correct voltage both sides? Test with the power off on the meters diode setting, probes one way should read 0.6 approx and the other way should be open circuit, if it's 0 both ways, the diode is dead.
Do either of the 2 yellow things beside the power wires (Thermal fuses) get hot when powering the board on? Do you have a multimeter on hand to check those diodes beside them as well? Circled in red
The plug will fit, however it needs to be the correct voltage. You may need to measure the output to your LED string while the string is connected, I suspect you will see something around 26V AC.
I can't suggest anything as I don't use Amazon, and have never had luck finding replacement plugs...
That one appears to be DC output according to it's specs. Unlikely to work but they may very well be confusing "DC" for the "AC" that it actually does output, as the polarity swaps to light up the LED's as their polarity in the wiring swaps every led to to give the "twinkle" or "chase" type effect.
The solar panel lights that contain 3 batteries often have a boost circuit to bring the light string up to around 26V AC, which causes the entire set to run dimly. The light string is a standard plug-in string minus the plug part, and instead has the solar panel.
Single cell solar panel lights...
Standard 31v 12W AC output christmas lighting adapter will do the trick for those solar lights. I've modified hundreds of sets (solar sucks lol)
Edit: AC because they'll be 2 wire type, if you use the adapter you linked they will fail or will not work right because
1: voltage is too high on the...
I would suggest Vixen3 for effects/sequences for dumb/non-addressable led strings. I've found it has far better support and easier setup for strings of lights as opposed to doing it all via Xlights. It is possible to do the whole music to lights sequencing in Xlights with non-addressable lights...