Wide World of Women

When I start winamp to play a song, the player disappears from the screen.
It doesn't just minimize to the task bar--it really disappears completely from the screen.
I can still hear the song going, but I'm not able to find the player itself.

What I noticed is that just simply opening the program (not even playing a song) is that it doesn't show up in the taskbar or the tray. When I start a song, the window stays up. It only "disappears" if I minimize it. Like you said, the song still plays, but it's nowhere to be found. The only way to bring the window back up is to double click the winamp.exe again. I have a shortcut on the desktop for that reason

Just for reference, I have version 5.5
Fairly old I'm sure. I really don't use it that often.

EDIT: Ah, never mind, I feel like a fool
Just go to Options --> Preferences and tick the boxes where you want it to show up