Mine is a similar vintage to yours, I believe. What are the symptoms, and what's the magic incantation to get Dell to give you a new one?

Symptom - turn on or come back from power save, and there's a flash and a pop from behind the power button. Thereafter it's dead.

As for getting the replacement under warranty, well, I'll tell you once I've been through it. Last time it was bellinghwoman who did all that.

It helps to have your invoice to hand - ours had a warranty number on it, which also helped.

I then started making phonecalls to Dell. You end up going through automated menu hell, but if you ignore questions that you can't answer, and choose the nearest options to your problem, you eventually get through to a human being.
It's probably best to start off with tech support - you can ring them on 0870 9080800 between 8am and 8pm, or I note from their website that there is an option to chat with them online - although that could be a bit difficult if your monitor has blown and you don't have a spare to hand...

The thing that got me was that although getting the replacement was no problem (delivered, on the date arranged, to bellinghman's workplace, to save me having to take a day off to sit at home and wait for it), I was originally told that they would collect the old monitor on a different date, so I boxed it up and bellinghman took it into his work so that it could be collected from there. The appointed day came and went with no sign of pickup - Dell use different couriers for delviery and pickup for some reason best known to themselves. Time dragged on, with the broken monitor gathering dust at bellinghman's workplace. After a couple of phonecalls to Dell's customer support it transpired that they had decided that it was not worth collecting, so I was left to dispose of it. Fortunately, the recycling place less that 2 minutes drive from bellinghman's work will take old monitors, so it was taken there.