Hiho,

basically, I played with a warrior earlier and leveled him up a bit (on Bnet). Created a rogue to try him out but couldn't log in. After I press "ok" on the name/password screen, the ok button greys out and nothing happens. The same happened afterwards to my warrior. Deleted the rogue but the problem persists.

/edit: When I want to create a new character, after confirming the password I want to set, it says: "You could not be logged on to the server with that account"

This is the error message I get when I want to create a new character. Logging in with an existing one will, as I said, time out. It will also give an error, saying I have put in a wrong password (which isn't the case).

You are supposed to hit up Blizzard Support, according to Blizzard, for B-net issues:

I had this happen too. The issue here is that you actually need a NEW ACCOUNT for every single character you create.
Exit the game first, then connect to battle.net, then create a new account for your Rogue. Now you will be able to log in.

What happened there is that you used your Warrior's login for the Rogue character, that caused the timeout, and after the timeout happens, you need to restart the game for the login to work again. I don't know the cause, just the solution.

You did miss the part where I said that I did that and if you look at my screenshot, it is actually from the account creation screen which didn't work.

Anyway, it is now working again, no clue why. I've tried everything, rebooting didn't work either and there was no Bnet issue in itself (another person logged in just fine). So...

I'm afraid you did miss the part where I said exit the game first. That's why it didn't work the first time and now it's working again. Anyway, enjoy the game.

I did exit the game, I tried everything after all (and rebooting required it obviously as well). It had nothing to do with what you said and is a different, unsolved problem.

i also seem to have this problem after not playing awhile. can't seem to login anymore, it just waits for a very long time after entering the password then says cannot join server. nothing was changed on my end, did not work before and after Hellfire update. i managed to login like once but after i switched character, restarted the game or PC i can't log in, so i really don't know what is going on.

Why did you delete your character? You can rename an existing character, retaining all items and statistics, just by logging in to a different battle.net account. This applies even if you create the new account just for this purpose.