http://bugs.winehq.org/show_bug.cgi?id=21451
--- Comment #5 from Kai Blaschke webmaster@thw-theorie.de 2010-01-24 16:48:40 --- Renaming/deleting the EVE\res\Audio\Jukebox\ folder so EVE can't find it's background music "fixes" the bug. This narrows the search down a bit I hope.
The splash screen/network problem looks like different bug. You should rather open a new report than posting it as a comment here.