thank you for your help, salt. to answer your questions...
yes, desktop awake.
yes, using the public ip address of my router.
yes, desktop is set up to allow connections although i use the option below (the more secure option) the one you have pictured.
interesting new development...it seems to be a firewall issue. even though i have "allowed" remote desktop. the connection never happens. when i shutdown the firewall, though, i am able to connect remotely. both through the home network and from outside. in both cases though i must use the port number i have opened.
so now there seems to be some reason windows firewall is blocking the connection even though i have allowed it?