I don't know if this can work, but I have two other suggestions.
Try to uninstall MP classic and reinstall it; maybe in this way the new install will force file associations. It worked for me with winamp (the reinstall corrected all file associations), I hope that can work also with MP classic.
The second one is a try to uninstall MP10.
Go to control panel and select "Add or Remove Programs". From here click on the "Add/Remove Windows Components" button. After it finish to load all installed components list, browse to find if you see mediaplayer 10 somewhere.
Beware: there are TWO media player installed in windows: the old version 6 (a standard of all windows versions), and the 10 version. I don't know if the version present in windows components is the 6 or the 10.
Try to uninstall it and see if this solve.
Hope this can help