Does it still happen in Troubleshoot Mode?

Yes, followed all directions there. I have cleared cookies, cleared history, added PBS website address allowing cookies, restarted firefox

It's working for me. What if you visit https://www.paperbackswap.com/index.php directly?

Does it still happen in a new profile? An easy way to get a new profile is to install Developer Edition and see if it happens there or refresh your existing profile.

Check that your accepting cookies by blocking or using Adblockers that can prevent your access to site that require cookies and since this is a registered login site they would require cookie tracking and block that can block your access to the site. Another is to use Firefox in Private Mode Browser to verify Addon aren't causing the login issue at the site.

When I disabled my adblocker, it did not effect getting into the site, so it is not the problem. Then I went to Private browser and entered the site address and it worked. The site appeared. What does this mean? How is this different from clearing cookies in your general instructions? Does this mean I can only use this site in Private mode?

Clear the Cache and remove the Cookies for websites that cause problems via the "3-bar" Firefox menu button (Settings).

"Remove the Cookies" for websites that cause problems:

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Data"

"Clear the Cache":

• Settings -> Privacy & Security
  Cookies and Site Data -> Clear Data -> [X] Cached Web Content -> Clear

• https://support.mozilla.org/en-US/kb/clear-cookies-and-site-data-firefox
• https://support.mozilla.org/en-US/kb/how-clear-firefox-cache

You can remove all data stored in Firefox for a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History -> Show All History" or "View -> Sidebar -> History").

Using "Forget About This Site" will remove all data stored in Firefox for this domain like history and cookies and passwords and exceptions and cache, so be cautious. If you have a password or other data for that domain that you do not want to lose, make sure to backup this data or make a note.

You can't recover from this 'forget' unless you have a backup of involved files.

If you revisit a 'forgotten' website, data for that website will be saved once again.

• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox

If clearing cookies doesn't help, it is possible that the cookies.sqlite file in the Firefox profile folder that stores the cookies got corrupted.

• rename/remove cookies.sqlite (cookies.sqlite.old) and when present delete cookies.sqlite-shm and cookies.sqlite-wal in the Firefox profile folder with Firefox closed in case cookies.sqlite got corrupted.
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

You can check for issues with Total Cookie Protection.

• https://support.mozilla.org/en-US/kb/total-cookie-protection-and-website-breakage-faq
• https://support.mozilla.org/en-US/kb/introducing-total-cookie-protection-standard-mode

I did the forget about this site process and then closed the tab linking to PBS and then restarted the computer. Then I typed in the website and tried to open and it worked. Thank you. I am going to save all the info you provided and the info on Total Cookie Protection in case this happens again.

One question concerning cookies.sqlite -> the directions above say rename/remove ... - so if I had tried that step would I be deleting that or renaming it and if so, to what - didn't seem clear.

We suggest to rename a file to make it possible to undo/revert such an action in case it doesn't work as opposed to deleting the file that doesn't allow this.