Time Capsule (A1355)

The power supply is likely dead.. but it can be main board faulty as well.

You will find it difficult to find replacements now.. loads on eBay but they mostly are early ones.. the later models used a Delta supply instead of the rather less reliable Flextronics.

It is now 9-10 years old.. frankly it is time to replace.

But if you wish you can do some real DIY work and replace the power supply entirely with External 12v plus internal 12v to 5v DC-DC regulator.

https://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems/apple-time-capsule-repair/new-issue-with-a1355-gen-3-tc

There are other pages with references to how to rebuild the power supply.

Even if you can rebuild or replace the power supply, you still have a 10+ year old hard drive on the Time Capsule that is frankly way overdue to fail.

If you need the data on the Time Capsule hard drive, you can pull it out and place it in a caddy or enclosure and copy all the data over to another newer hard drive.