Use the ping utility to determine if you're connected to other hosts.
For example:
ping isp.com
On success, ping displays something like this:
PING isp.com (10.0.0.1): 56 data bytes 64 bytes from 10.0.0.1: icmp_seq=0 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=1 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=2 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=3 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=4 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=5 ttl=255 time=0 ms 64 bytes from 10.0.0.1: icmp_seq=6 ttl=255 time=0 ms
This report continues until you terminate ping, for example, by pressing Ctrl–C.