Hi. I need help to understand and repair this problem:

My laptop (vista) has had the black screen blue box saying "Enter Current Password" for about a year now. It used to appear only when I clicked the power/sleep button. Now it appears after I startup. I have two accounts that are both passworded and I enter the administrato account password to get past it.
Recently I also have a random black window appear.

I can no longer use a physical LAN line connection and it has nothing to do with the server (they said my adaptor was faulty?)

In the past my computer has also prompted me to System Restore.
I had an issue also with the renaming of a user folder that completely wiped that user off and I had to just copy and paste files into a new account.. (this happened long after the ' current password thing' so is this related at all?)

NOW my computer has crashed (Blue Screen) several times and I have no idea what to do... Help? I have no idea about computers

Sounds like the best course of action would be to back up you personal data and rebuild it.
Windows does benefit from an occasional clear out to factory settings..

Is there anything I could do short of wiping it clean?

Seriously, you could spend days cleaning it up, but you would be better of starting over from scratch.
Vista is a bag of pooh and suffers heavily from cludge.