Okay Adywan, I explained the scenario to my mate who sells in 'Currys' and also to someone else that I know is knowledgeable in my local 'PC World' too. I'll just post the points here for the benefit of others here that may buy expensive equipment in future -
Both of them reckoned it seems unlikely that the 'extra 3' that was advertised at the time would have been for only 3 'months' rather than 3 'years', if you're sure that it didn't explicitly say so. Most stores/companies normally offer 'years' of extra cover, not 'months' they said. So that's definately a point that can be argued more yet, since it seems the promotion was ambiguous.
As far as the 'Warranty card' being missing from the packaging, it's unfortunate it wasn't included due to someone's error. They both agreed that it's the last thing most people concern themselves to look for when they open things up, themselves included. Ideally, it would be spotted as missing at the time, before something breaks down, but as you were told the 'receipt' covered you, it's not surprising you didn't concern yourself with that.
Both of them confirmed that a basic 'receipt' only covers anyone for 1 year, but think you should continue to argue the fact that you paid for what you believed was 3 'years' extra cover, not 3 'months'.
The other point they said they would argue if it was them, is this - since you still have the 'receipt', they recommend that an equally valid complaint route on top of the 'warranty' thing....is to emphasise that 18 months is too short a 'shelf-life' for an expensive monitor to last anyway. So they said that you should make a fuss over that aspect too, and complain that is wholly inadequate, and 'not fit for purpose'.
They suggest getting onto the 'Gateway' customer service, either directly or online. They also think it might be worth contacting 'Trading Standards' again to point this out, as you may have just got someone unhelpful the first time.
(and it might be best to omit telling anyone that you've been using it every waking hour for the last 18 months....ahem)
Either way, both reckoned that they would certainly 'escalate things' with both the store and 'Gateway'.
Good luck, and I guess we'll all now know to query the sellers about the whole 'Warranty card'/'extra cover' scenario a bit more in future, at the point when we first pay for something.