You have to read almost to the end of your question to discover that it was a used car when you bought it - rather than new.
Even if it was new, you would not be able to demand a replacement, as in law, you would have to give the seller 'due opportunity' to remedy the fault.
With a used, (5 year old) car, it would be unreasonable to expect the same degree of reliabilty as a brand new car, and also unreasonable not to expect to replace some part or other through "fair wear and tear".
The "guarantee" that accompanied the sale was an incentive, and has no legal requirements as to what it must cover - you should check for yourself as to exactly what is 'guaranteed'.
(Bear in mind that many things that go wrong could not unreasonably be expected to happen in a car of that age, and therefore be deemed to be "fair wear and tear" and therefore not covered.)
Remember also that, being a used car, the dealer could quite legally have sold it "as seen" - (though it must be road-worthy if sold as such).
Unfortunately, I think you are being a bit unrealistic in expecting a replacement - you could try for a part-ex (on their terms, inevitably) - or you could try and persuade them to perhaps waive some, or all of the repair cost.
This is why, to a non-mechanic (like myself), buying a used car can, at best, be pot luck, and at worst - a bloody nightmare.
Good luck, and caveat emptor!!