Suszter, this answer has helped others, hopefully it will help you as well.

The menu buttons as 3 parallel lines (toaster menu) usually means your existing menu won't fit in the available space, if you make the menu items smaller or allow more room for the menu items in the template they should appear and then you can tweek the result. When I am doing this type of upgrade I set the site to non-responsive. When I get it right I again turn on responsive and play with the headers/footers and layout for the various resolutions.