OK, Kev's sweated enough on this one, I can reveal some additional information which Kev didn't know about...
What they never made clear was that it was turning over too slowly for it to start, whether using battery, another battery, or jumpstarting. Thats how they found it was aux belt slipping on a/c pulley.
So, Kev, you weren't given the full info to be able to correctly diagnose....
And that'll do for me. Thanks Jamie.
Now as Columbo says, "Just one more thing...", Looking at the post i made after your duff description....
If the fuel pump isn't running while it's turning over then it's the crankshaft sensor. I'd bet my left bollock on it.
Also, It wouldn't cough no matter what you sprayed in there, cos if it doesn't know what angle the crank is at, it won't generate a spark either.
* EDIT * You'll also need a working EML to paperclip it.
Why wasn't that fuel pump running? Does a seized compressor stop the fuel pump from running? Does a seized compressor inhibit spark generation? New one on me if that's the case.
Was the pump maybe ok, and was running, but you gave false information? Yep, probably.
I still reckon the V6 lump would still fire, even with a seized compressor, it'd just burn up an Aux belt. MarksDTM concurred with me on this point also.
So i can sleep easy, knowing that i made the correct diagnosis for the information that was presented before me, which was, at best, patchy.