My time capsule 2TB Model A1409

Perhaps.

There are specific hardware and software requirements for both Macs: Use your iMac as a display with target display mode - Apple Support. The Mini must be a 2019 or earlier model and must be running Catalina or earlier macOS version.

It's no substitute for Target Display Mode but you can use Screen Sharing: Share the screen of another Mac - Apple Support.

If the TC's power cord is providing correct voltage phase and frequency yet its LED remains dark, then its internal power supply has failed.

Would really make no sense to replace the power supply unless you also replace the hard drive, which is also overdue to fail. Apple will not handle repairs.....even if you are willing to pay them.....but a local repair shop could probably handle things for you.

https://www.ebay.com/itm/133876739053

[Link Edited by Moderator]

Guess the forum moderators will not allow instructions for repairs, since the link I provided was removed.

Yes, with difficulty.

And yes while you're in there I'd also replace the hard disk drive with a larger capacity one. $100 buys a 5 or 6 TB hard disk these days.

The fan is certain to need cleaning.

Guess the forum moderators will not allow instructions for repairs, since the link I provided was removed.

It won't be hard to find 😉

👍

When you get it fixed I'd appreciate hearing how everything worked out.