Last month I got a new Mac Computer 10.8.4 and my Apple Time Capsule stopped working/well it would not let me into the Time Capsule. My Internet was still working though.
If you're having the same problem here is how I fixed mine.
Go to Applications/Utilities/Airport Utility, click on it.
Click upgrade firmware
It will say your connection is going to be temporarily unavailable, don't worry that is normal. Click yes and it will update your firmware.
After it is finished you should be able to now open your Time Capsule again.
once it has updated it will look like the above image
now go to your time capsule by opening finder and then click on the Time Capsule,
it should open and reveal the contents.
After you open it you should see the data folder, open that folder
There you go you are all finished and now set it up to be backed up using Time Machine if you wish.
Have a great day Mac friends!