This makes no sense whatsoever.
Both my Macs in this office have the same Mail Preferences now: using the same server at one ISP to send and receive emails.
I now find that one Mac cannot send emails but the other one can and does. The settings are identical.
This may be related to a problem I ran into trying to get my iPad (and later an iPhone) to check mail on my personal domain. Rather than bore you with all the hair-pulling and mysterious symptoms I ran into, I'll cut to the chase.
What I learned was that my domain's mail server would not allow simultaneous SSL connections from the same IP address to the same port number for IMAP. All the devices behind my NAT router appear, to the server, to be coming from the same IP address.
SSL+IMAP is supposed to use port 993, but the server in question would also allow SSL+IMAP over port 143, so my current workaround is: my desktop computers connect to port 143, and only one of them is ever running Mail.app at any one time. My iPad and iPhone both connect to port 993 (the iPhone in particular not liking non-standard ports), and I only ever check mail from one or the other at home.
When I'm away from home, there's no problem. When the iDevices are not behind my NAT router, they appear to be coming from different IP addresses, and can fetch mail simultaneously. (I can test this at home by turning off WiFi on an iDevice, forcing it to be "away from home".)
It's not a problem with my NAT router (an Airport Extreme Base Station), because MobileMe and GMail both work as expected, allowing simultaneous SSL+IMAP access from all my devices, even through the router.
The point is, the problem may be not in your settings, but in your mail provider's settings.
One test is to quit your mail program on the machine where it works, and see if mail starts working (after a decent delay and perhaps some prodding) on the other.
(OTOH, I notice you say your problem is in
sending mail, which has nothing to do with IMAP. Still, the symptoms I was seeing were so baffling before I finally figured out what was happening that it was difficult to get a good handle on what was and wasn't working. Maybe an actual problem with IMAP is spilling over into an apparent problem with sending mail.)