Can this modem work on a gateway laptop?

when you have the ethernet cable connected, does the pc activity light on the modem flash? if not, the driver may be disabled, or bad. try running a usb cable and downloading drivers for that. if you are trying to go wireless, then you will need a seperate router, as this modem doesnt have wireless capability

No... wait...

Do youe a dial-up service? or do you have a cable network?
This modem is for a cable system, like Comcast or Time Warner.

If you need a dial-up modem like the one in your laptop, then obtain a USB modem from Best Buy, Fry's, Office MAX/Depot:
like a "Zoom" or "SupraMax" or "US Robotics" brand, 56K v.92 modem.