Thanks for the help! I didn't get to post before I had to go to work yesterday. We did what both of you said (looked at an disassembled valve on doityourself.com); used two wrenches, used the nut from the old valve
The problem with the old valve was that the valve stem had gotten stuck some how and stopped working. We took the insides of the new valve and just put them inside the old one. Couldn't use the new one because it was the screw-on type and the old one was a "pop-on" type. So far as of this post, the valve works just fine.
If there is anything we should know ("should have not done that", "better replace the entire valve", etc), please let us know.
Thanks!
Lucrosus