In order to DJ with Live, you need two seperate (preferably stereo) outputs, although two mono outputs will also work. So your sound card needs low latency drivers. Sounds like you don't have a sound card other than the native Viao card, so go to
www.asio4all.com and download the driver for the Viao. Then set up Live so that you are using the Crossfader underneath the master fader and set up tracks as either A or B so you can crossfade between tracks.
Connect your output from the Viao to the mixer, but seperate the left and right channels into seperate mixer channels, so you can use one channel to monitor and cue, and use the other channel to play out.
This is, however, fairly ghetto, and given that you've spent money on a BCR and a laptop and a mixer, the least you can do is buy yourself a decent sound card. Emu, Presonus, and Maudio all make decent USB or Firewire cards, and Echo makes a good PCMCIA card, all of which can be had around $300. Then you have multple outputs to cue and play and mix and match, such that you won't even need yout mixer other than to pump out the main bus from Live.
If you have any questions, please read the manual first. We're here to help, but you'll need to do a bit of work too.

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