I cannot log into the website for my health insurance. Except... I sorta can.

I have been logging in to that website for more than 10 years without difficulties, but last week after putting in the Username and Password, I would go to the "Login" button, the little hand-thingie (sorry for the technical talk) showed that the computer recognized the button as clickable, I would click it... and nothing.

I actually received some competent help from the website tech support guy, who suggested I try logging in from a different computer. I braced myself for the ordeal of having to use SWMBO's Macintosh [Eewww...] and logged into the website without difficulty.

Tech guy then said if I cleared all my browser history and cookies (I use Firefox) then it would work from my computer. I did that, but the situation remained unchanged.

Then I remembered that I also had Microsoft Edge on my computer, left over from a brief period where Amazon wouldn't let me "Download and Transfer using USB" when I bought eBooks from them, but a bit of research showed that Microsoft Edge would do it. (Firefox fixed that problem a few weeks later.)

Anyway, my computer will log onto the website using Microsoft Edge but not Firefox. SWMBO's computer will log onto the website with Firefox and probably Chrome (I didn't try it).

After deleting my browser history and cookies and restarting the computer, why won't Firefox log into the website?

tanstaafl.

Probably because it's much stricter about allowing third-party scripts and cookies on your computer.

Go to "Settings -> Privacy & Security" and (temporarily) set "Enhanced Tracking Protection" to "Standard". If that works, you've found the problem. Set it back to "Strict" and then add an exception.

To add an exception for your health insurance website, browse to it and then click the shield icon in the address bar. Flip the toggle switch to turn enhanced protection off.

There is a chance that the web site has some kind of a coding quirk which stopped it working under Firefox. Maybe the site designers have only tested it with Chrome and Edge. If so, though, you'd think their tech guy would know that (unless it was a recent regression that the support team is not yet aware of).

I think it more likely that you've got a firefox plugin that's interfering. In Chrome, I use both AdBlock Plus and UBlock Origin, and on rare occasions I have to disable one or both of those plugins for certain web sites to work. Things like login screens are often where that sort of issue is most noticeable.