OK, if I understand it, the "new" window is System Prefs? What happens if you close/quit System prefs before shutdown/Restart and then Start up again?
The shade asking if you want to install another version of a Panel you already have installed is normal...when you have double-clicked a Panel you may have recently downloaded or one that is still available for double-clicking. Double-clicking a downloaded ".prefPane" file is how they are sometimes installed (the other way being to simply put it into the ~/Library/PreferencePanes folder.
I'd still like to see a screen-shot of your Login Items list.
Finally, note that when you select Shutdown or Restart, there is a checkbox (selected by default) that asks if you want windows that are open to re-open on the next Start/Restart. I've heard/read that the global choice of
not Resuming
doesn't seem to affect that checkbox. I don't even know where a setting is to turn Resume off globally... Probably in one of
Paddy's links. Although one of the options in Lion Tweaks turns it off in individual apps of your choice.