OK, Dark, I'd try this. Uninstall WMP 10. Download
CCleaner and use it to clean your system; be sure to include the Issues scan, which checks the registry and identifies registry entries that should be deleted. Alternatively, or in addition to CCleaner, download
Eusing Free Registry Cleaner 1.0. After you've used one or both - and I'm inclined to recommend using both - then reinstall WMP 10 and see whether you can add the Mini-Player.
Note: the installation of CCleaner will also install the Yahoo toolbar unless you opt not to install it, which you can do by simply unchecking a box that you'll see on a screen soon after the installation procedure starts. I'd recommend unchecking the box.