There should only be one way that each of the connectors can plug in on the transformer block. The wires with the 'eye' on the end (they should be green) are ground and should be placed on the studs that stick out of the top of the transformer block. There are small nuts that hold them in place.
As far as the actual board repair, the first place to start on any Atari board from that era is to replace the sockets with new ones. That will fix probably 80% of the problems you see on these boards. If you aren't comfortable doing the repair yourself, I'd find someone that can. Do the simple stuff first and hopefully save yourself some headaches!