Have you checked via FTP on your server.
Is the folder for the Skin you want to delete still on your server?
If it is, back it up and then delete it.

Yes, skin folder is in the server, and listed when i want to chose a skin, but not when i click on "manage skins".

In the Admin area... what skin is selected from the drop down menu in Blog Settings -> Features and the section called Skin and style [Admin]
Is your new skin listed in that drop down list?

This might sound like a funny question, but does the skin that's installed but not available on the Global settings->Skins install tab have a screenshot file? If not you might want to copy the screenshot from either evopress or custom over to that skin's folder (the root of the skin - not skinname/img folder) and see if that makes it show up.

I have no idea why I think this might matter.

Oh and go to your Tools->misc tab and delete the pre-rendered cache. It's some kind of mystical thing that I think helps when weirdness sets in.

EDIT: it's "skinshot.png" - not screenshot.

I deleted some of default skins, then reinstalled them, and everyones (including my skin) are now correctly displayed.
Don't know the reason... some kind of mistery...