Tom.
1.  Run winamp
2. Press control-p  for the winamp prefferences.
This will open a list view of dialogs.

2.  The first one is "general, which is the one you want.
3. The 7th tab is "show splash screen, this should be unchecked.
4.  The 9th tab, is "check for new versions at Startup, tghis should be 
unchecked.
The 12th tab is system tray, this should be unchecked.
5. Press enter to close the prefferences and save your changes.
I am thinking their might be the dialog asking download new winamp? Y or N. 
So you might have to press N befor you can press control-p to get in to the 
prefferences.
Let us know if this works?