How do I get Finder windows to reopen on start up?

There might be several answers to that.

• Your restore for finder could be corrupted somehow. Delete the ~/Library/Saved Application State/com.apple.finder.savedState and give it a try
• Your finder app may be configured NOT to restore the windows. Try this: defaults write com.apple.finder NSQuitAlwaysKeepsWindows -bool true

Does your other apps have the same behaviour? Have you tried with another username to see how it goes?

Sources:

• http://osxdaily.com/2011/07/17/delete-specific-application-saved-states-from-mac-os-x-10-7-lion-resume/
• http://hints.macworld.com/article.php?story=20110722125937252