Hi Joy, welcome to TechIMO.
A modem basically just converts a digital signal for your computer, whereas a router will dispatch these signals to as many as 254 different machines. Your modem is a combo modem/router. All you really need to send a wireless connection to a laptop in another room is this item:
Walmart.com: Qwest W1000 DSL Wireless Expansion Module by Actiontec: Computers How to install the W1000 wireless module for the the M1000 Qwest DSL Modem | eHow.com
A laptop is a good choice as it will almost certainly already have a wireless adapter built in.
All the instruction you need is found here:
Internet Help | Modems | Actiontec M1000 | Landing Page
That said, we are always here if you need us.
There are many ways to connect a laptop to a TV. S-Video connections work well enough and are rather common, though you may need a
1/8" stereo jack to dual RCA jacks for sound. These are also quite cheap and easily found at Radio Shack, but wait until you have the laptop in hand before buying adapters or cables.
If you already have the TV, you should consider what ports are available before buying a laptop.