OK, Just found the solution, and I'm a "happy bunny"!

I had two problems: -

1) For some reason the XPUIPC.ini file had lost the IP address of my computer, but setting this after running "IPCONFIG" to check what it should be didn't work.

2) I had omitted to run Plan-G in "Administrator mode" when re-installing it as a separate copy for X-Plane.

(Posted here in case anyone else has the same problems.)

Affirm! (Yes I researched this forum, and thought I'd found my mistake - downloaded it, then when I came to install it found it already there! I had forgotten that I'd already installed it!)

I've managed to "mess up" the connection between PlanG and XPlane 10.
In doing so I also messed up the connection to FSX!
As PlanG has always worked for me "straight out of the box" I took the easy way out - Uninstalled and started afresh. FSX connection now works perfectly again.
Nervous of messing up the FSX connection I installed (into another folder) a second copy of PlanG for use with XPlane 10.
It still refuses to connect to XPlane - it gives a "double boing" rather than the single one I expect when connecting to FSX, the toolbar indicates that it's connected as the "disconnect" button becomes active, but there is no Large yellow aeroplane Icon to indicate my location.
However when flying on VATSIM I manage to get a rough fix on my position as clicking on the "VATSIM" button shows my location as the normal "other traffic" icon (The little blue one rather than the large yellow one). This is a "static fix" as the data doesn't seem to get updated unless I disconnect PlanG from VATSIM and re-connect to get the next "rough fix" of my location.
I've obviously done something daft, but can't work out what! (I have a vague memory of it all working perfectly when I first installed XPlane 10 a couple of months ago and tried a flight "off-line", but can't be absolutely sure, so it might just be wishful thinking.)
I have tried the obvious things - eg making sure the user aircraft option boxes are all ticked on the set-up page/tab and have run out of ideas to try. - Any advice/suggestions would be gratefully received.
Plan-G_Log.txt (hopefully) attached