Apple is now offering free repairs or replacements for Time Capsules bought between February and June 2008. According to an Apple Knowledge Base article (http://support.apple.com/kb/TS3351), some Time Capsules sold between approximately February 2008 and June 2008 may not power on or may shut down unexpectedly after starting up.
Some Time Capsules with serial numbers in the following range may be affected: XX807XXXXXX – XX814XXXXXX. The serial number is located on a gray strip on the bottom of the device.
If your Time Capsule falls within serial number range above and it does not power on or shuts down unexpectedly after starting up, it may be eligible for repair or replacement. If Apple or an Apple Authorized Service Provider confirms that your Time Capsule is affected, Apple will repair or replace it free of charge.