Dear Dobner and others, I found out what the problem was. By going to Ping.fm and carefully reading what the instructions were, I realized that Ping shortens the URL automatically all by themselves. That's right, you don't need to sign up for Bit.ly or any of the others if you are going through Ping.fm.
So, if you are using Shorten2Ping and you are not getting your URL's to show up, go back and take off the setting to shorten the permalinks with any other service, set that to "Nothing" and then give it a try. I think you will find that Ping.fm will shorten them all by itself.
Putting one other shortening service in there (like Bit.ly) just sort of countermands the way that Ping operates and so the link doesn't show up at all.
This worked for me, I hope it works for you. Shorten2Ping is a great plug in. ¡Muchas gracias, Sr. Aguilera!