Are you using a crossfader, like SQRSoft Crossfader? This can often cause problems, because as far as I know crossfaders "buffer" a song -that is, read up what is coming ahead, so they can mix the end of one song with the next one. This is usually a good idea, but MD doesn't like having the crossfader on - like you said, it will go crazy through all the presets for as long as you've set the buffer (about 10 sec) and because it isn't giving MD the right part of the song, so to speak, and the beats will look way off even once it starts. The default Winamp output plugin is NullSoft waveout I think (it's the top output plugin on my screen), the buffer is set at 2 sec by default, so usually that is how long it takes MD to start reacting (which will obviously change if you change the buffer).
If that's not the problem, then post back, but hopefully that works (if that's what you did), and hopefully I actually explained that right, sometimes I have thought I have understood something only to be corrected
Post back again about whether this worked..