Several sites are reporting that Apple has issued a Knowledge Base article in the Support Forums that notes that some Time Capsules sold between February and June of 2008 are
subject to a recall eligible for possible repair or replacement due to the problems described. Should you have a Time Capsule with a serial number in the range XX807XXXXXX – XX814XXXXXX that's experiencing the dreaded "shutdown and never power up" problem, it's time to either go to your local Apple Store with the device (after making an appointment at the Genius Bar, of course), visit a local Apple Authorized Service Provider, or to call the Apple Contact Center for your country to find out what to do.
If your Time Capsule has died and it's in the suspect serial number range, the company
will may either repair or replace it to get it back up and running. That is good news for those who have lost the ability to back up their data automatically using the Mac OS X backup utility, Time Machine. Good luck!