AGGGHHHH! DO NOT DISCONNECT THE BATTERY while the engine is running! That is a real easy way to destroy stuff on the car. The generator can have all kinds of different problems yet the engine will stay running without the battery so that test is meaningless. It was a trick done many years ago by untrained mechanics who didn't understand how these simple systems work.
First of all, what kind of car? Year, model, engine size, etc.
Second, you're doing yourself a disservice by piggybacking on this post. Only I will get an automated e-mail telling me a reply has been posted and it will direct me back here. No one else is going to see your question or have the chance to respond. I'll help you if I can but I'm not an expert on all cars and models.
Please consider a to help us answer more questions.
Saturday, April 28th, 2012 AT 9:50 PM