If they're using a pre-8 version of Windows and Internet Explorer, the IE has a wizard/tool that will run even off line to test connectivity problems. If the problem is down the line, this won't help; but, if there's a modem/router issue, the diagnostic will find it. I have used it several times after I'd been on-line and was disconnected. It turned out those times to be a stagnant connection in my modem. Re-setting the plugs into the jacks and the trouble went away. Just sitting there, contacts get crud deposited on them from the air and they need to be re-established every few months (seems the PC designers put all the power supply fans in a spot to drag high volumes of air by the modem jacks, visiting them with a lifetime one-tenth of a normal phone connection). Then there's that silicon dust from the Iceland volcano to clean away.
REM the 4 W's: Whence Worknot, Wire Wiggle
(exercising due safety of course!)
"...Tomorrow's come a long way to help you."
Tim Davis 'Your Saving Grace' Steve Miller Band (1969)
"...Yesterday's at least a mile back."
Dale Peters 'Dreaming in the Country' James Gang (1971)