On all 4 computers?? I find that hard to believe, especially when, on the newest computer (a laptop that I just bought about a month ago), I simply installed winamp, and didn't change a single setting because I wanted to verify that the shuffle problem wasn't being caused by anything "unique" that I was doing on my other 3 computers. All I did after the installation from the admin account, was log off, log on to the guest account, open up winamp, select the "winamp modern" skin (because it prompts you for a skin choice when you first run winamp), add about 10 songs to the playlist, turn on shuffle, push play, and begin pushing "next" to see if songs were picked randomly or in the unwanted order that I describe in the original post.
I'll try this when I get home, but I'm doubtful it'll work. Regardless, thanks for the tip.