Its getting too complicated MarkF, in that box there are at the back two cables with 3 conductors each (blk, red, wht) + 2 more cables with 2 conductors each. The box is rally packed. One of the 2 cables with the 3 is feeding the 3-way switch and the rest I can't figure out where they are going - too difficult to see.
Your schematic has the wires to the light after the switch and in my case the light is in the middle of the run, don't know if it makes a difference.
Just called a local company to have the switch installed and forget about it and we are talking about +200.00 for a visit!!! So forget about paying this kind of money to have a switch installed
My schematic has the light in the middle of the run just like your wiring:

As for wires, you have two sets of three conductor wires (one set goes to the switch you're working on the other to the middle 3-way switch). You say there's two sets of two conductor wires. One of these must go to the single switch and the other must be power coming into the box. At a minimum the single switch on the left will have both of one of the sets of two connected to it (power, light, or whatever all at the other end). Should be easy enough to see. The other option is that the single switch and both 3-way switches are powered from the second set of two wires.
You said you traced the black wire on the dark switch terminal and the black wire (of three conductor) to the neutral. Are they both going to the one of the two conductor cables?
If this power coming in is wired correct, your light should be working. Near as I can tell, both 3-way switches and the light are wired correctly and match my schematic. It's now just the power feed.
Do you have a black and a white wire on the single switch on the left? Or two black wires?
The 3-way switch in the middle, do all three wires from three conductor cable go to each of the three screws? (i.e. is it wired like your corridor 3-way switch?)