I bought a Sony VAIO VGN-FE770G recently with Windows XP Media Center 2002 installed. I pluged the ethernet cable on it (was working fine on ACER laptop), but nothing happens. The message that the connectivity is limited or null show up to me. I have DHCP enabled. Tried static IP with no succes.

Can someone help me?

Modem is: Motorola SURFboard® SB5120 Cable Modem. (this is router too?)

Have you unplugged the cable modem for a few minutes? Those devices (Motorolas) typically to ARP caching to speed up the initial device connection, and this can cause problems when switching attached NICs. Power down the cable modem for a few, then turn it back on and attach it to the new machine - it should work.