The never ending load screen could be an add-on issue. Go ahead and uninstall your addons and try to log in again. To fully remove your add-ons, do the the following in this specific order:
Exit the game
Navigate to C:\Users\<username>\Documents\Elder Scrolls Online\live in windows explorer
Rename Addons to Addons.old
Rename SavedVariables to SavedVariables.old
Check in-game to see if the if the issues persist.
If the issue does not persist, then one of your add-ons is creating the issue. Try re-enabling your preferred add-ons one-by-one in order to determine which is causing the problem.
Changing game settings back to default can also help If the issue persists:
Open the game and go to the settings menu [Esc].
Go to each subsection, Social, Gameplay, etc. and reset all settings to defaults.
Once this is done, try starting the game again.
If after resetting to default and clearing your add-ons and the issue continues, turn off your PC completely, reboot your router and try again.