I started my 2004 discovery and went back in the house for about 10 miins, when i returned it was not running !!! I went to crank it again and it coughed and spluttered trying to start but did not. Now i just turn the engine over and does not fire up, I take it I do not have a factory engine immobiliser fitted. Please help i've only owned this for 2 weeks or so !!!

 

There are lots of posts on this one, most likely it is the crank sensor.
When it gets hot it shuts the engine off, when it fails completly it wont start at all.
The cam sensor is the next big one and then the fuel pump.
Before you replace anything check for spark. And also listen for the fuel pump kicking on when you turn the key to the "II" position.

Remove a spark plug, reattached the plug wire and then have a friend trun the engine over, does it spark?

 

I just pressed the fuel cut off reset button, now when i crank it it seems like it wants to start, like there's fuel starvation i.e. not getting through. where is the fuel pump located??

 

The fuel pump is in the back under the cargo floor. Turn off the radio, open the cargo door and stand and listen while your wife turns the key to the "II" position, you should here the fuel pump kick on.
It will only run for a few seconds and then shut back off.

 

It does not appear that the fuel pump is coming on. I think it is located under the car next to the rear prop shaft. Could it be immobilised ? which is cutting off the fuel pump ?

 

Well it could be the fuel pump is toast, but I would check it for power first, pull up the carpet to the cargo area and you will find a access hatch for the fuel pump, open the hatch and then check for power to the pump, then check the relays for the fuel pump and also check the fuse for the fuel pump.
I guess check the fuse first, under the drivers dash. There might also be a fuse for it under the hood, not sure on that one.

 

How much gas is in the truck?
And I just thought of something, according to Tacomatech (hes a LR mechanic) when the crank sensor goes bad the engine will not get any fuel.When the cam sensotr goes bad there will be no spark.
So check the fuel pump for power first, and then go from there. The crank sensor is cheaper than the fuel pump.