Micheal's solution is a good one that will usually work. It's never a bad idea to pick up a router when you have more than one computer. The modem that the cable company gives you then communicates with the router, and the router communicates with all your devices. This will save you the hassle of having to unplug one to plug in the other.
To power down the modem, simply unplug it at the device itself and wait about 10 - 15 seconds. This is usually sufficient to let it completely cycle through. I just had a crazy thought. Are you using a networking cable or a USB cable to connect the modem to your laptop?
Example of an Ethernet Cable Example of a USB A/B cable
I ask this because if you're using the USB cable to connect your computer to your modem, you really do need to power cycle the modem each time you switch computers. Also, you need to make sure that you have all the software that came with your modem installed on both computers. If you're connected via Ethernet, you don't need any drivers for your modem, but if it's USB, then you have to have the drivers installed for it to work properly.