Bizarre that one computer would work and the other wouldn't. You're sure that both are logged into your router (and one of them isn't on the neighbor's Wi-Fi or something)?
I'm having this problem with Comcast, and their "support" is so ignorant that they think it's because my reply-to E-mail address isn't a Comcast one. They seriously don't understand that outgoing and incoming E-mail is handled by different servers. They even thought that I could authenticate to the Comcast outgoing server with the user ID and password for my E-mail account at my domain host (which has nothing to do with Comcast).
Unfotunately those Apple docs posted above don't address this problem.
I'm having similar issues with a client's computer network of imacs and macbooks. Same network, but the imac consistantly states that the smtp server for Comcast is offline in the mail app at least. On that same computer, Thunderbird works flawlessly. The Mail app works fine on the other macbooks. I'm at a loss almost having tried alot of settings. You would think that if the several other mac products work with a certain set of settings that the one iMac would work too....I'm starting to think that maybe its the Mail app itself in this case.
What was the SMTP error?
Comcast has messed up their outgoing server somehow. I got a message about "The sender address firstname.lastname@example.org" was rejected by the server smtp.comcast.net." This of course is absurd, since YOUR E-mail address has nothing to do with sending mail.
If that's the problem, you're going to have to call Comcast and repeatedly escalate the case until you can find someone with even a basic understanding of how E-mail works. I had to get a "supervisor" involved, and this person was still so ignorant that she had to call me back the next day after "researching" the problem and still proposing asinine attempts to resolve it. And it never did get fixed, by the time I left the location at which I needed to use Comcast.
You need to insist that your reply-to address is irrelevant for sending E-mail. If you're connected directly to Comcast's network (which you are when you're connected through your cable modem), you should be able to send through their SMTP server. Period. That's how Time-Warner and Verizon work, for example. The first thing you're going to hear is "Well, you're not using your Comcast E-mail account." IRRELEVANT. And why would anyone use the obscure Comcast-assigned E-mail address in 2013?
I have Comcast, and thank goodness, I'm not having your problems currently. I have had problems in the past with email accounts, and like you, I have two Macs. So I took the MP downstairs next to the iMac, and just went through every single setting in Mail Preferences > Accounts. It was one typo. But it could have been one bad proxy setting, or anything else.
I would recommend you do that.
Best wishes for a solution.
Had this issue once and found this to be the solution:
1. Open Mail and then open Preferences.
2. Select the Comcast account.
3. In the Account Information pane select the Outgoing
Mail Server dropdown and choose Edit SMTP Server list.
4. Select the account and then select Advanced tab.
5. Insure that authetication is Password and the correct user name
is entered and that you have entered the correct password if
it is there at all.
It appears that during account creation in Mail, that the password is not
always added to the outgoing SMTP box or sometimes gets removed
Woodmeister50's post (almost a year old) told me what I need to know. Periodically the Comcast outgoing mail server becomes unavailable (i.e., goes offline and Connection Doctor shows an error). To get it back, I have to go in and re-enter my Comcast password. (Running Apple Mail on OS X 10.8.5)
Apparently, this is a lot easier than explaining the problem to Comcast (let alone expecting them to fix it).