Hi and welcome to FpcH
I must state that I am no expert on the legalities of warranties.
If it refused to boot up from taking it out of the box then it is not fit for purpose.
As far as I am aware - you are entitled to a replacement.
Repair should not be an option because it was sold to you "not working".
You expect a working computer if this is what you have exchanged your money for.
If it is not working out of the box - it is not a computer!
Did you buy this direct from Dell or from a Supplier ?
If you bought it from a supplier then
they are responsible for the replacement as your contract ( i.e. they are selling a pc and you exchange money for it ) is with them.
If this is the case - phone the firm > explain that it never worked and you have been trying to get Dell to replace it.
Explain that you now know it is their responsibility and you would like a replacement.
Be sure of your rights.
Contact the local Citizens Advice Bureau.
You may find this useful.
http://www.moneysavingexpert.com/shopping/consumer-rights-refunds-exchange
You have had the machine for longer than a month so a refund may be out of the question.
However, the firm must prove that the pc was NOT faulty when you bought it.
They will have a job doing this - unless they demonstrated it to you.
A small claims court is ( apparently ) easy to take a firm to.
In your case - I can see no way that you could lose.
They would, I am sure, resolve the problem to your satisfaction if threatened with this.
If you are going to threaten this - you must be prepared to go through with it.