One thing is for sure, I didn't find Roadrunner's
http://help.rr.com/HMSLogic/emailhelptopic.aspx to be very helpful.
For the heck of it, for outgoing mail port, try custom port instead of default port and enter 25, 465, or 587 singly each one at a time and see if that buys you anything. If they use SSL (and that wasn't apparent to me from their help page whether they do or not) you would likely want to try username/password authentication for smtp.
Also, you might take a peek in Keychain Access and delete any existing entries that pertain to anything wi.rr.com. Mail would then re-prompt you for that account login information when it attempts to connect to the smtp or pop servers.
If the old computer was Leopard, have you tried copying over your $HOME/Library/Mail and $HOME/Library/Mail Downloads folders and your $HOME/Library/Preferences/com.apple.mail.plist file to the new computer?
Have you called the ISP and told them that the old computer works fine and the new computer with identical account settings doesn't and that you would like to doublecheck with them the account settings (type of account is POP? what is POP port?, what is SMTP port? verify pop and smtp server names, using SSL on POP? On SMTP? Do they use password authentication on SMTP? (If they use "None" that implies they use the WAN IP address to authenticate -- if its one of theirs, your good)
I don't think reinstalling Mail will gain you anything.
At least we know who the ISP and mail provider is, maybe another user/helper that has the same provider can weigh in here. I do not use rr.com so any other advice from me at this point would be like drawing random straws.