Update:
Trying the whole process using ethernet plugged in!
This is what I've just found.
Firstly, running my iLok and Pro Tools on my Macbook Pro WORKS PERFECTLY! Everything is as it should be (that's with Pro Tools 10...I haven't installed 11 on this machine).
Reading other folks' experiences, I decided to combine these and start from scratch.
Firstly, WIRELESS.
So, reformatted a drive, reinstalled Mountain Lion 10.8.2, installed iLok Licence Manager, installed Pro Tools 10.3.6. NO LUCK.
HOWEVER!...... repeated the whole process, using a WIRED connection (ie ethernet cable connected to router).
Reformatted drive, reinstalled Mountain Lion 10.8.2, installed ILM, then PT 10 and guess what.......booted PT no problems!!!!
So, the issue appears to be with ILM requiring a wired connection (on my desktop) to check licencing etc.
As soon as I unplugged ethernet, although I'm still online wireless, PTools will not boot.
Therefore, I am making progress!!!!!
The funniest thing, is that on my MacBook Pro, WIRELESSLY, it is FINE.
I hope this helps someone work out a permanent solution.
Eco