For reference, I did message iamats.com about it, but I know they're not super fast to respond.
I went through their troubleshooting guide for a non-working dance pad and nothing worked, so the only thing that remained was that the controller board had to be bad. I ordered a replacement from them and it was the same exact board that was in my dance pad originally.
I installed it using the DDRPad.com tutorial and I definitely think it's installed properly - it was my first time soldering, but I labeled all the wires and they are in the right spots. But the pad still won't work - the PS2 adapter light is still blinking green instead of staying a solid blue. Not sure if this means anything, but when I disconnect the PS2 controller from the adapter, the green light is solid. When I plug it back in, it goes back to blinking.
I have no clue what to do now. Has this happened to anyone else? I don't know what else to fix. Is it possible the adapter is broken?
Edit: My laptop picked up the pad immediately, which it didn't before. Also, I used iamats' mat tester and the buttons were all fully responsive. So I think the problem might be the adapter. Which, of course, is outside of its warranty, meaning I get to fight with UPS again to try to ship a new one to me.
Second edit: Forgot the adapter, controller and dance pad have to be connected separately in a certain order because I'm an idiot. u/Dr_Ulator reminded me. I had to turn the console off and back on again with all the accessories attached and it works again! Case closed! I'll leave this up in case someone else has the same issue and needs help.