Most residential ISPs (internet providers) allow only one modem to connect to their network. They usually have to "provision" the modem, or allow/authorize its' MAC address on their network. So, to answer your question no, you can't simply hook up another modem and have it work.
If you can't reach the destination with a wired ethernet cable, the next best thing is setting up some type of wireless connection. There are many wireless routers/access points/client adapters that can work, you will need a wifi device on both ends. Usually people set up a wireless router next to their cable/DSL modem to serve many wireless client devices. Many client devices like your laptop and Xbox 360 already may have built-in wireless client adapters, so they can connect to a wifi network.