I found a solution!
When I put the code: is_home() && !is_paged() it all worked out as I wanted it to!
Unfortunately, that don’t seem to work either. But thanks for the help!
I really don’t get this… 🙁
The site is http://aaronaxelsson.com/ if that’s any help, and it’s the widget with a pic and text just under the header that I’m trying to fix.