I had these problems with Tiscali, notably when I was younger playing Operation Flashpoint online, kept getting booted off the server!
Try opening your run command (windows key + R), typing 'cmd', then 'ping
www.google.com' or 'ping 66.249.91.99'.
If it says a reply was found it shows you are connected.
Eg.
c: \>ping
www.Google.com
Pinging
www.Google.com [66.249.91.99] with 32 bytes of data:
Reply from 66.249.91.99: bytes=32 time=19ms TTL=239
Reply from 66.249.91.99: bytes=32 time=19ms TTL=239
Reply from 66.249.91.99: bytes=32 time=22ms TTL=239
Reply from 66.249.91.99: bytes=32 time=19ms TTL=239
Ping statistics for 66.249.91.99:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 19ms, Maximum = 22ms, Average = 19ms