My mac does not see time capsule even when connected by USB

Let me just add to Bob's helpful post..

Time Machine will say it is going to do a new backup but will in fact discover the existing backup at the point where it starts.. it will then take an age two ages and half an age.. (to put it in biblical terms) to verify and check where it last got to.. and do the next incremental.. be patient.. it does work.. mostly.. except..

EXCEPT where you have High Sierra.. do you?

If you upgraded to HS from Yosemite you profile is showing.. then you might also need to fully reset Time Machine.

See

Re: Time Capsule backing up one computer but not the other

which explains the verify bit as well.

In fact with High Sierra.. (almost any version El Capo onwards really) if you really want to keep the old backup I recommend you archive it.. use archive function in the airport utility to a USB drive of equal size to the TC disk.. and once that is complete erase the TC and start a fresh clean backup.

If you held the reset button for 7-8 seconds while the Time Capsule was powered on, then you performed a Hard Reset......which erased all of the network settings on the Time Capsule and returned them to factory default settings. The good news is that a Hard Reset does not have any effect on the data stored on the Time Capsule hard drive.

A USB connection from the Time Capsule to your Mac will not work, so do not attempt this. The USB port on the Time Capsule is there only to add an additional hard drive for additional storage.

So, you will need to try to set up the Time Capsule again, just like you did when you set it up originally. You can use the same device name, wireless network name, passwords, etc that you used before if you wish, or set up the Time Capsule with new names and passwords.

Once that has been completed, you will need to set up Time Machine again to back up your Mac to the Time Caspule as follows:

Click the Time Machine "clock" icon at the top of the Mac's screen

Click on Open Time Machine Preferences

Click on Select Disk, or it might say Add or Remove Disk

Select the current backup disk to highlight it, then click Remove Disk

Restart your Mac

Open Time Machine Preferences

Click on Select Disk

Select your Time Capsule disk, which is likely named "Data"

Click Use Disk or Use for Backups

Time Machine should start a new backup again within a few minutes