During a demo today could not use Messages for video chat or screen share - what dumb thing was I doing wrong?

Question

I was giving a demo / class today for some people in a volunteer group I work for. They all got new MacBook Airs or MacBook Pros, and I got a MacBook Pro because I am going to be going into explain how to use them.
Most everythng went well, but one really cool thing I do all the time from home on my iMac I couldn't get to work. That part of the lesson was a disaster, though fortunately everything else went well.
I'd like to figure out what dumb thing I was doing wrong so I can show them next week.
I know we have to sign in with AOL accounts for screen sharing to work in Messages. So first I had everybody sign up for a free AOL account. That went fine.
Then we all logged in using our accounts. That went fine for everybody except one person. We could all see each other online, with little video cameras next to our names in the Buddy List. One person never showed up anywhere for some reason.
But we could not do either video chats or successfully request to share other peoples' screens, which I do all the time at home to help other people with their Macs.
One person could not even see any requests from me pop up. One person could see my requests come in and accepted them, but nothing happened after that.
Ordinary message chats were working ok.
Things I already thought of:
1. Perhaps the wi-fi in the bulding was blocking some ports? Just in case, I turned on mobile hotspot (tethering) on my iPhone 5 and had everybody connect to my network. But the results were the same, so it wasn't that.
2. I wasn't sure it mattered, but in Settings > Sharing I made sure that everbody had screen sharing turned on. And just in case, even though I don't have this set from home, I further made sure everybody had "anyone may request to control the screen" checked.
While I could do local network sharing of screens (via the Devices list in the Finder side panel), I couldn't for the life of me get it to work with Messages. But I've been doing this for years from home to help my sister and other people across town with their Mac by doing screen sharing this way and taking over their screen.
It must be something dumb I'm overlooking. Anybody know what it is?
Thanks,
Doug

Answer 1

Problem solved, finally, by AppleCare support!
I gave up trying to reach the "English support line" guy located in Manila and decided to insist on plain old Japanese support here in Tokyo and explained the problem from scratch.
First we tried all the usual suspects, but nothing we did could get it to work. Then we did an ARA (Apple Remote Access) support session. This was the first time I ever did this. Quite cool, and very useful.
At first we still could not figure out what was wrong, but finally isolated the problem to the way my AOL account name was entered.
When I added the AOL account to my Messages app, all I did was enter my username part. I didn't add the @aol.com part, because I never did that on my iMac. However, Messages kept on automatically adding "@aol.com" to the end of the AIM account name.
The Apple tech person got me to try once again to get rid of the @aol.com part of the account name. We:
1. Disabled the account.
2. Manually deleted the @aol.com, leaving just my AIM name.
3. Restarted my MacBook Pro (very quick, by the way, and also immediately brought back his ARA session).
This time the @aol.com part remained gone, and I was able to test connecting to my iMac, which has a different AIM account set. It worked!
I was able to do screen sharing via Messages! And also do video chat via Messages. Yay!
So much thanks to Watabe-san at Apple support. The people I am teaching will be happy to see this working on Sunday, because it really is a very useful tool for assisting people remotely.
doug