My 2TB TimeCapsule will NOT finish backup

What is the make & model of the Comcast provide modem or gateway device? Do you have your Time Capsule (TC) connected to this device by Ethernet (wire) or by wireless? How do you have the TC configured: router or bridge? Will you be using a MacBook Pro, running OS X Mountain Lion, to administer this base station ... as per your tagline?

Can I use a USB to USB cable to hardwire my laptop to the Time Capsule to back up?

No.. the USB port on the TC is used for printer or external hard disk only.

The TC is a network device.. you must connect to it via ethernet or wifi.

Since you have now upgraded (so called) to high sierra you will experience issues.. this is expected for OS as Sierra and later greatly increased network security.

Our STRONG recommendation is to use a USB drive.. 2TB self powered 2.5" drives are great, cheap, reliable.

Use that for the moment.

If you wish to use the TC.. get Carbon Copy Cloner or similar 3rd party backup software. Time Machine is just too difficult now to network targets.

I bought a new 2TB Apple Time Capsule Feb 27 because my TC from 2015 "died".

You are still in the 14day return window.. Just.. IMHO just return it. The issues it is causing you are such that I would just buy the external drive.. and a different wireless router.

Could this be I have a weak router?

You are in a different.. rental place.. and some places seem to sink wifi.. like a black hole it vacuums in all aspects to make your life easy. (Part of the wifi voodoo)

I doubt your TC is different to any other.. within normal manufacturing tolerances.. however.. I have had 4 of the current model TC.. my current one is no.3 and it is a lot better than any other for wifi. Proving it would be difficult. And in a new place it is hard to say it is better or worse than previous one you owned.