This sounds like a problem with your cookie settings in your web browser. Not a problem with your internet service or connectivity.
To see if this is the problem, log out and log in as the Guest selectable from the login screen and attempt to log in via firefox from there.
Alternatively install an alternative browser and attempt to log in from for example; Chromium instead.
If you can sucessfully log in, then you must change the settings in your firefox browser to allow your sites to store cookies. If you don't have many bookmarks or important history you could just delete the .mozilla directory in your home folder (show hidden files first). Otherwise you should go into the profferences for firefox and allow cookies for those sites.
I'd also check to see if you have any extensions which could cause these issues.