I found a bug. If I turn off second screen in my laptop (the external one) and switch to single screen (the on that is built in my laptop), then opera reopens. BTW, this occurs when external screen works as main screen when connected, I don't know what happens in other cases.
@burnout426, thank you for your work! I tried out all tricks except comparing the cookies with other browsers. Unfortunately it didn't help. I will do this comparing when I have more time.