It shouldn't conflict. The Page ID and App ID's are separate IDs to Facebook and it shouldn't have a problem if you're using the right ID in the right place. Basically, the App ID should only be used in the configuration area of the JFBConnect component. The Page ID should only be used as a parameter in the JFBCFan module.
Also, if hardcoding it fixes it, you'll have to explain that some more. I'm not sure why the parameter wouldn't work. Either way, we'll figure out a problem, just a little confused about what's happening right now.
As always, if you can send a link, that helps

Thanks!