if your LAN works fine and your laptop connects fine, network the machines use the laptop to download then just transfer files across.
or download to the laptop and burn a disc (if the laptop has a burner of course)
or use a usb mini drive if you have one. 64 mb should be plenty to move a couple files across.
i have found that adaware alone doesn't get all the adware. used in conjunction with
spybot it gets most stuff though.
i wouldnt bother reinstalling zonealarm until you get the throughput problem solved. just uninstall or disable it. the less stuff in the way of your internet connection the better while trouble shooting this.