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;
http://www.microsoft.com/downloads/details.aspx?displaylang=en&FamilyID=ea541e8e-85a3-4d2f-a3a4-b329d03fc2fa