Your Gen1 TC power supply is dying.
It is being very gracious to you.. like the drowning person it bobs to the surface a few times.. to shout help.. help!! Are you listening?
Soon .. very soon.. it will go under.. I strongly recommend you copy off all files you might actually want. If just backups. probably don't worry but any files you stored there.. are about to be lost.
Apple do not repair and it is out of warranty so will not replace.
If you want it fixed it can be.. by a repairer..
http://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems /apple-time-capsule-repairers
Or you can do it yourself if you have some basic soldering skills.
The instructions are there on the site.
A new one is $300 odd.. and a lot better in terms of disk size and wireless. But is probably about equal reliability.