OK, if the standard Finder windows are not minimizing it says something about the interface preferences may be corrupted or there is system level corruption which be caused by some internal hardware issues. Make sure your data is backed up, and when you are, we can go and attempt to repair the system.
To backup your data, see this FAQ:
http://www.macmaps.com/backup.html
Disclaimer: Reference to links I make to my Macmaps.com website are a for your information only type reference. I do not get any profit from this page, and it is open to the public.