Well rather bizarrely, it looks like the red wire is negative, and the green wire positive? - and the protection diode is directly across the incoming supply with no fuse?.
First thing you need to remove the remains of the protection diode - and as long as while you're working on it you ONLY use it on the mains, you can't accidentally reverse the power again.
The last two pictures show a biggish capacitor on the bottom of the board, this is the reservoir capacitor - with the protection diode removed, and the unit plugged in the mains, measure the voltage across that capacitor - it should be around 15V to 20V or so. If it is, then the unit will probably work?.
If the voltage isn't there, check on the red and green wires coming in - and see if it's there. The DC voltage from the mains unit goes through a switch on the DC input socket, so you could check on there as well if it's still missing.
Assuming doing this gets it working?, then you should replace the protection diode - and I would seriously advise fitting a fuse as well - in the green wire from socket to PCB.