I have posted abut this before, a really annoying bug cosidering a New Order quest.

This quest won't start at all. I have finished Bloodline by refusing Harkon's gift and got banished. After that, nothing happens. Bloodline quest is marked as finished, but there is no new quest available.

I then went back to Fort Dawnguard, but there is no vampire attack, and speaking with Isran doesn't bring new discussion options.

I had some saves however, and reloaded, then started Bloodline again. This didn't help.

I tried to use the console, typing 'setstage DLC1hunterbaseintro 20', but that does nothing either.

This is a real game-stopping bug. Is there anything that could be done? Could this bug be because I have several mods installed? I have also tried to disable them, but that didn't help either.

Go back to before you started mucking around with console commands, if you are sure disabling all your mods did not help, just go do something else and come back later. Things do not always start straight away, go explore the fort a bit or do another quest, then go back occasionally to see if any other options come up.

Yes, I have tried to move aroud and do few quests after that. Could it be that all mods need to be disabled Before starting Bloodline, or even the Dawnguard itself?

Some mods will affect Dawnguard, you just have to try it out for yourself, even if you disable them it can still have an effect. If you have a follower with you try dismissing them, and see if that helps.