You can take the top off the cut out and see what the condition of the insides are. You can also manually operate the cut out with the top off or use a jumper wire to bypass the cut out. If the points are burned you can try to clean them. I prefer to replace the cut out with a self contained, cut out looking regulator from here:
http://www.funprojects.com/products/10505v.cfm
If the cut out isn't the problem, you will get to disassemble the generator and look further. Most likely either the brushes need replacing, which is easy and cheap, or someone put the battery in backward and burned up the generator, which is not so easy and not so cheap.