A
warranty is legally a 'gift' from the manufacturer (or retailer). As such, it can be as generous or restrictive as the provider of that warranty cares to make it. For example, it's perfectly legal for the provider of a warranty to state that they'll only repair your purchase if you return it personally to the Chinese factory where it was made at 3am on a Sunday, while standing stark naked and singing the Albanian national anthem backwards.
So if the warranty you've been given excludes the reinstallation of Windows there's absolutely nothing you can do about it. (The retailer and/or manufacturer was never obliged to offer you any form of warranty anyway).
However a warranty is completely separate to your STATUTORY RIGHTS, which might well be relevant here. Under those rights a retailer is obliged to repair or replace a product which goes wrong DUE TO AN INHERENT FAULT, possibly for up to 6 years from the date of purchase.
An 'inherent fault' is something which was actually wrong with the product when you bought it, such as the use of poor quality components or poor workmanship. (So if your PC has developed problems due to having a hard drive which wasn't up to the job you'll be covered. However if the problems relate to software which was installed after you bought the PC, or to a virus, then you won't be covered).
If a problem develops within the FIRST 6 MONTHS after purchase then the law automatically assumes that it must be due to an inherent fault. You simply need to tell the retailer that, for example, your hard drive has failed and he must replace it, ensuring that he doesn't leave you disadvantaged because of the problem. (i.e. he must refund any carriage costs you incur and must reinstall Windows).
AFTER 6 MONTHS the retailer still remains obliged to repair or replace an item which has developed a problem due to an inherent fault (without you being left at a disadvantage) but there's no longer an automatic assumption that it was such a fault which caused the problem. (i.e. the retailer can refuse to repair/replace the item unless you get an independent report to show that an inherent fault was to blame for its failure).
http://www.which.co.uk/consumer-rights/regulation/consumer-rights-act