I swear I sent a test message from her machine yesterday afternoon. But I've already deleted it since there was no point in keeping it...
But, if both accounts are broken, it seems more likely that somethings rotten in Denmarkher MBP! But I'm not wasting more time changing/resetting/modifying her prefs for hours on end as I did Thursday, only to be told the problem was on their end. 
QUOTE
the problem is that you owe me a recipe
OK, ok...<Community Forum Post>
OK, finally fixed. Mostly my fault (what's gnu?!). I re-entered the Mindspring info almost completely wrong. Once that was straightened out...
All her info is now engraved on a large stone...The smtp server is smtpauth.EarthLink.net (nothing about Mindsrping in there)
Her username is actually her email address, including the "@" and the domain
The outgoing port is now set at 587 instead of the multiple choice set (which includes 587)

Comcast was just a matter of finding the correct info...
Moral: Don't rely on an app that uses info to also keep it! At least not Mail...