Sabine,
That's definitely not good, and not something we've ever heard of. We always recommend backing up before upgrading, but honestly, that's been precautionary. There shouldn't be any reason that 4.1.1 should be killing your site like that.
Regarding the App Id, with the 4.1 release, we actually made the key even less necessary than before... so that shouldn't be it. The only reason you should need one is if you're using the login functionality, the Page Tabe/Canvas integration, or the new Requests feature. The social buttons or front-end widgets almost all do not require the App ID.
When you can't access the admin area, was it just JFBConnect, or was it your whole site? If it was just the JFBC Overview area, it's likely that you don't have cURL enabled within PHP. If it's the whole site, I'm not sure what could be causing that. If you install again, please set error reporting to Maximum in the global configuration area first. Then, if you get a white page, there should be a PHP error that states what's wrong. Send us that error, and we'll help figure out the issue.
It's getting late here, but I'll be on for about 2 more hours. If not, I'll be on again in the morning.. in case you want to do it at a time that you know someone is around to answer questions.
Sorry for the troubles, but we'll get you going,
Alex