Wave Runner,
Despite your good intentions, you would not legally be allowed to work for free. You would have to commit yourself to filling out all the paperwork as a normal employee, receive some form of monetary compensation, and at the employer's discretion, work for longer than just a few weeks. As Peter said, it would cost them too much money to take you on for such a short time. It's usually several months before a business recoups the cost of training an employee.
- red.november