Time Capsule disk repair - how?

Unfortunately, the message that you see almost always appears because the hard drive is failing, or has failed. If the hard drive is physically damaged, repairs to the Time Capsule hard drive are not possible unless the drive is actually removed from the Time Capsule. Repairs.....(if possible).....are then made and the drive is reinstalled in the Time Capsule. There are no guarantees that the data stored on the Time Capsule can be saved in this type of service.......(which is extremely expensive).....far more than the original cost of the Time Capsule.

Assuming that the hard drive is physically OK......(not likely)......and the "repairs" need to be made to the files that store the data on the Time Capsule, you could try using Disk Utility on your Mac to check and see if Disk First Aid can repair the damaged data files. Worth a try if you keep your expectations very low. Post back if you want to try this.

If that is not successful.......(which unfortunately will likely be the result).......you could try erasing the Time Capsule hard drive and starting over again to see if that type of operation will get things going again. If this is not successful, it will confirm that the Time Capsule hard drive is physically damaged.

If the Time Capsule is 4-5 years old or older, my advice would be to recycle the Time Capsule since the power supply inside the Time Capsule is also suspect about this time. In other words, it would not be wise to pay for extremely expensive repairs to the Time Capsule hard drive unless you also have the power supply inside the Time Capsule replaced as well. To keep things in perspective, you could buy a refurbished Time Capsule for a fraction of the cost of repairs.

The easiest, fastest, least expensive and most reliable way to back up your Mac is simply connect a USB drive directly to your Mac and back up that way.

Unfortunately, since the Time Capsule hard drive cannot even be accessed to try to make file repairs or erase the disk, this confirms that you have a hardware issue with the Time Capsule hard drive.