So your old mother calls and says she cant connect to the Internet, bummer you have to go through hoops to make her open a command prompt, ping this and that and before you know it you have spent an hour or more.

Well Windows today actually has a decent looking utility for testing network connectivity (it may be enough for that initial test), and this may thus be worth a look before getting into the command prompt.

The utility is here;
C:WINDOWSNetwork Diagnosticxpnetdiag.exe

Or you can get it from here;