Time capsule help needed- unable to access

I have tried to connect it to a Mac via the usb plug and it isn't showing up in finder

It will never show up in the Finder using the USB port on the back of the Time Capsule. That port is only there to add another USB drive for additional storage or connect a USB printer.

Connect an Ethernet cable from your Mac to one of the three LAN <--> ports on the back of the Time Capsule. If your Mac does not have an Ethernet port, you will need to use an appropriate adapter.

The exception is that it does appear in the list of wifi networks.

Not recommending that you do this, but it is possible to connect the Mac to the Wi-Fi signal provided by the Time Capsule. To do this though, you would need to know the password for the wireless network that the Time Capsule is providing, so there is that.

Or is it faulty?

Possibly. The A1355 version of the Time Capsule was discontinued in June 2011, so the Time Capsule (and hard drive inside the Time Capsule) are at least 13 years old and as much as 15+ depending on when the Time Capsule was placed into service.

If all else fails, the only thing left to try is reset the Time Capsule back to factory default settings and then set it up again to work on the network that is in use there. This will not affect any of the data on the Time Capsule hard drive, so if the Time Capsule is working correctly, the data on the hard drive should be visible.

But.....getting at that data using any of the methods above is going to be another can of worms. In other words, you will be able to "see" the hard drive using the Finder, but opening the hard drive will be another challenge. We'll have to try to cross that bridge when we come to it.

The best option by far.....and likely your only option at this point.....would be an Ethernet connection between the Mac and Time Capsule, but that will require using an adapter if the Mac does not have an Ethernet port. This will be a much faster connection than trying to use wireless.

If you don't know the password for the wireless network that the Time Capsule is providing, that will of course not allow the Mac to connect to the Time Capsule using Wi-Fi.

But.....no matter whether you are trying to use Ethernet or Wi-Fi to connect to the Time Capsule, you might be asked to provide the Time Capsule disk password to allow the Mac to open the Time Capsule drive. It all depends on how the Time Capsule was set up originally.

If that is the case, then the only option will now be to reset the Time Capsule and set it up again using names and passwords that you write down to remember them. Post back if you need help with this.