If it is less than 3 years old and you have applecare then Apple will replace it.
Otherwise they will not touch it. It is a consumable.. so you buy a new one.
If you want the old one repaired Apple cannot help, but you can remove the hard drive if you have stuff you want.. you can also replace the power supply with an external or repair the internal one.
http://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems /apple-time-capsule-repair
For a TC of that age and disk size a new 2TB is good value. You can get the dead one fixed and sell it off, or just sell it dead.. they fetch reasonable prices on ebay.. if you don't want your information available, open it and wipe the hard disk using a USB holder. They get around $100 for that age and disk size working.. more or less, depending on the ebay day. Maybe $50 dead.
A repairer can fix it and put a larger hard drive in it.. but that will cost near to 2/3 of a new one.. so doubt it is worth it.. although IMHO the repaired one can last longer than the new one. As we can fix the fundamental flaw.. it runs too hot.
Contact a repairer near you if the nature of the repair is beyond you.
http://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems /apple-time-capsule-repairers