Is the "network card" a wired ethernet one or "wireless"?
If it is "wireless" and only 802.11g (54Mbps), it won't be fast enough to handle a 50Mbps broadband connection. A "wired" ethernet connection running at 100Mbps shouldn't have a problem and neither should an 802.11n "wireless" adapter running at 150Mbps or 300Mbps (in conjunction with a compatible 802.11n router).
While online, go into the Network Connections folder, double click the connection that is in use and look at the 'speed' that's shown. This will be the port speed at which the PC is connecting to the router.