[Stickman]

PEPS can be a pain when it stops working!
The padlock light can come on if the steering lock is a bit sticky - try wobbling the wheel a bit to unload it and pressing the start stop button.
Failing that, hold the fob by the padlock sign on the column (where the barrel would be if it had one) and try the start button. That's a short range override of the main detection system.

 

[Stickman]

So is it locking/unlocking on the fob, or does it just recognise the fob from outside to let you open the door and let you lock it by touching the handle?
I presume you've tried both fobs?
I know it queries the fob again to put the ignition on so could be something to do with the aerial inside.

 

[Stickman]

Actually just had another thought too, it should close the windows if you lock it by touching the handle and keeping your finger there (like it does off the fob).

 

[Stickman]

Well the windows are controlled by the REC, but I suspect the thing to make them drop is the Open and Start unit which is just next to it. Might be worth a check to make sure all connections are made properly. In the boot on the left. There are some fuses that serve the Open and Start unit too which it wouldn't hurt to check, 16 and 33 in the REC, and 16 in the UEC.
I think you're right, fix the ignition problem and everything else will follow.

 

[Stickman]

?? The Clarkson method of electrical engineering.

The windows probably aren't going back up after dropping to open as they've lost their home setting. Once you get it sorted you'll need to reset them by holding the button down at the top and bottom of transit.
Doesn't help with getting it to recognise the key though to get the ignition on.