I have a similar problem (win7). Winamp was installed for 1 year so, always had the latest updates ok, but after upgrading to the latest release 5.6.x.. I can only view the classic skin.
I went to Control Panel\Appearance and Personalization\Display, but my font settings are 100%
So.. any idea why this happens ? Help appreciated.
PS: After it happened, and as a tentative to recover, I noticed all the skins were gone from the skin directory, (weird) so I went to a backup and restored the skins, and now I can select them but even so, the GUI always displays the classic view, although in the skins menu item, my chosen skin is checked (V).
Restarting Winamp does not fix it.