Hi Andy,
I'm a bit confused here -- if you are using an old project you may have actual data (actual start, actual finish etc) which prevent the dates from changing.
You note the dates "screw up" when you try to create a new start date.
So, first step is to save the existing project as a template through File > Save As and select Template from the File Type drop down.
You should get a message asking what you want to remove from the file, select all data necessary including any actual data.
If you have removed the tasks constraints, you should now be able to set a new project start date through Project > Project Information.
Give that a try and let us know how you get along. Any further information about specifically what "screws" up -- what you expect and what happens will also help.