You're SURE there's no file called com.apple.Stickies.plist in your ~/Library/Preferences folder? (Just to reiterate, and apologies if I'm insulting your intelligence, but we are talking the Preferences folder in your Library folder in your Home directory).
It's certainly not impossible that Stickies could keep its data files in the application bundle, but it seems at least a bit odd that Stickies on my system would have a data file in the Preferences folder (it's 547 bytes, and its modification date looks about right in terms of when I last used Stickies), but yours doesn't. And I'm pretty sure this has been Stickies' behavior at least since the public beta.
This is a long shot, but could there be a permissions problem with either the ~/Library folder or the Preferences folder? You might want to make sure that you have read/write/execute privileges for both folders...
Just as an experiment, you might try copying the Stickies.plist file from your laptop to your desktop computer, just to see what happens.