Can't log in with my I-phone.
No problem logging in with my laptop.
Checked all the settings, changed password.
When I enter screenname and password the "Log me in" icon is not "highlighted".

I logged off on my iPhone and logged back in. The button didn’t highlight for me either.

I'm guessing it's your iPhone blocking you from logging in without https/SSL.
I double checked and there's nothing on our end that would prevent that button from working.

Apple really likes to mess with it's customer base.

I have no trouble logging in from my iPhone using the 'log me in' option under the 'Log In' section. It doesn't need to be highlighted to select it. If you haven't entered correct or complete info, it will tell you.
Are you using the native browser (Safari) or something else?
Try opening in Safari's Private Mode, too, just to ensure it's not caching old creds somehow (click the 2overlapping squares at the bottom right corner, then select 'Private' near the bottom of the screen).

Make sure your iOS is up to date.

I have the same problem with my iPhone…couldn’t log in for about a week. Still can’t get in using google. Tried logging in on my iPhone with Duck Duck Go and it went right through.?

My iPhone works just fine logging in here

Thanks @SirAndy for checking.