Looking for a program to send an SMS message to my cell phone whenever
a destination address cannot be pinged.  Tips for free solutions. 
Expensive solutions are not an option.

Of course there are costly solutions (ipMonitor) which do exactly what
you're looking for, but if you want a free solution you can try Server
Check by NetMechanic
(http://www.netmechanic.com/products/SCP_FreeSample.shtml)

This will test your site for 8 hours, at 15 minute intervals, and
email you if the site goes down.

I know you're looking for SMS, but in my experience, many providers
(such as Rogers, here in Canada) will provide all cell users with an
SMS email address, such as #########@pci.rogers.com, which acts just
like SMS.

If this works for you, you could potentially set up a macro to run
every 8 hours that would sign you up for a new demo?  Just a thougt,
and it's free.

JFFNMS can do that and much, much more.

http://www.jffnms.org/