My problem is that I have a large breadboard for prototyping. I can not fit the breadboard into the case.
For prototyping what?
I have a LCD with a chip and do not want to solder it to a PCB board.
Then don't. Is the chip on its shoulder?
Does anybody have a idea that does not include soldering?
An idea about what? I have an idea about what I will do tomorrow that does not involve soldering, but it is not likely to help you.