Well, I seem to be the only one to have this problem so far.
Like I said earlier, I tried to reinstal Premiere by first not forgetting to deactivate any application to reinitialize the adobe key, just in case. Then I uninstalled the Premiere Pro Family through the Windows control panel. Rebooted and reinstalled it through the Adobe Application Manager. But still, it didn't work. So I had to resort to a complete system restore. Luckily I had a recent backup.
I have Premiere working now! I guess we'll wait till it happens again to figure this one out.
The only thing I can see that caused the problem in the first place is that a file must have gotten corrupted at some point.
But why only Premiere?