Just looking in the manual, I see where it says you can do it by pressing the enter key but you have to have the radio set to Tone Squelch. I've got my 780 programmed up with military aviation frequencies and I haven't fooled with any kind of tone programming on it and so long that I can't even remember how it was done. But it looks like if you have what is in the center of this screenshot, where it talks about Tone Data and Tone Squelch, turned on it should work. You obviously don't have key lock turned on since you mentioned going into the menu. Unless there's something else I'm not remembering, and that is very possible, I don't remember anything else that ever gave me any problems with saving the tone to memory when I used to use the radio a lot.
One other thing I just thought about may or may not be related? When I turn on my 780 I get static when I turn the volume up or down because I need to get some contact cleaner and spray the radio contacts. Since it's a 20-year radio, I'm wondering if your Enter key might have any kind of problem like that? Well I doubt that would be the issue I thought I'd mention it anyway. It would be easy to check.
Brian (COMMSCAN)