Did you set up Homegroup for networking in Windows 7?
Homegroup only works with Windows 7 computers and will not talk to your XP computer.
If so, you will need to change the networking system to one that XP can use.
On your Windows 7 computer, click the Start button at the bottom left of the screen, then go to the Control Panel and choose Network and Sharing Center. Click the link under "view your active networks" (if you've set up a Homegroup,the link should say "home network").
In the next window choose "Work network" that will switch you from a homegroup to a workgroup so your two computers can talk to each other. Before you can network the computers, you must assign the same workgroup name to both of them and SHARE folders in Explorer.
The XP computer's internet problem is not related the above. If your broadband modem is connected to the router and the router is connected to each computer your should not have any problems. If you are using a wireless connection you may have changed the ID or keyword when you installed the Win 7 computer.