Is the external modem connected to this system? Do you hear it dialing?
Are you getting an IP address? You can verify this with the command: IPCONFIG /ALL
Can you ping the default gateway? You can do this with the command: PING XXX.XXX.XXX.XXX, where the X's are your IP address.
If all that works, see if you can ping a site by name, such as :PING TECHREPUBLIC.COM, which should resolve to this on your system:
Pinging techrepublic.com [216.239.115.148] with 32 bytes of data:
Reply from 216.239.115.148: bytes=32 time=77ms TTL=239
Reply from 216.239.115.148: bytes=32 time=77ms TTL=239
Reply from 216.239.115.148: bytes=32 time=77ms TTL=239
Reply from 216.239.115.148: bytes=32 time=77ms TTL=239
Ping statistics for 216.239.115.148:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 77ms, Maximum = 77ms, Average = 77ms
Try that first.