Does this issue affect ALL select boxes on the Admin / Host pages, or only certain ones? Are other input elements (e. g. text input fields, checkboxes, ...) affected as well? If it concerns all select boxes, I still guess it's a CSS issue, but perhaps I suggested to search at the wrong place.
In your first post you said that you have that problem with several skins. So if it's caused by a wrong CSS definition, it must be in the portal.css (which contains the CSS that you can edit with the Stylesheet Editor in the Site Settings. Search there again for any select {} definitions. Such a definition is not part of the default portal.css as it is delivered with the installation pack, and to give select boxes a fixed height doesn't make sense, but perhaps it creeped in accidently during development?
If you have more than one portal in your DNN installation, and that problem occurs in other portals as well, you should search in the _default.css. If you don't find anything, then I think it's some strange kind of configuration problem, and you should re-ask your question in the configuration forum.
If background and foreground colors for select boxes were identical, as brought up in other answers, you should be able to see at least the border of the select box, which is not the case as I far as I can recognize it on your screenshot. Also, you should then be able to select the entries, even if they are invisible.