First those wires don't look right ,their should be a plug on the speaker for a harness .
Also i am not sure the wires colours are right either but i have no clue anymore as i don;t have oem wire on my car.
They are not supposed to be soldered , i would guess someone changed them at some point in time.
If the back doesn't work right now try listeing to the rears on only. Now see which one will make slightly more noise than the other and which sounds more distored at the volume needed to play.
Cut one of the wires on the speaker which sounds bad, you can fix it later .If the other side returns to normal then it is that speaker. If not put it back together and try the other side. You only need to cut one of the wires not both.
If disconnecting either doesn;t help then it is either you amp or deck but from the looks of it it is one of your aftermarket speakers