Okay, tcshaffer - I have solved my problem and hopefully this will solve yours too. It was a plugin that was messing me up - for me it was the WordPress SEO by Yoast plugin. Here's what I did to find out which one it was (i have about 20 plugins in all).
I first noted which ones were "Active" right now. Then I deactivated all of them. Then I went back to my draft post and hilited a word, clicked on the link icon, inserted the url into the pop up box and voila! It linked and worked! Then I went back to Plugins and activated the first one, switched back to Posts & highlited a word, hit the link icon, inserted url and it worked. So i went back down to Plugins and activated the 2nd plugin, then back up to Posts and tried it out again - it worked. And so on, activating each plugin and then retesting in Posts until they were all done except the last one.
It was the last one that when I turned it on, then tried the link, it didn't work. That one for me was WordPress SEO by Yoast. To be fair the plugin site does say it's in Beta with no guarantees to work. Good luck! (and PS - don't go see Bad Teacher)