Spent an evening with this thing. +30V after rectifier diode, +4V on controller chip Vdd. Also +30V on LED+ and 1.2V with 4V control pulse packets on LED-. That look, erm... fine. Maybe the real problem is in friend's LED string? It might become damaged after using it two years outside house. I'll ask him to bring one of his used LED strips me too.
Found a bug in my reverse engineering - LED mode switching actually happen by shorting PIC pins 4 and 5 to ground through push button. Corrected and uploaded reversed circuit here.
Got curious about current return path. Found no actual way for current return in negative side. The only visible connecting is via controller chip GPIO-s that seems very wrong for 2A current. Maybe I missed some trace, but have no idea where it is.