Cannot Set Up AOL IMAP on Two Laptops Using Apple Mail

What a pain it has been to migrate over. I have actually looked forward to migrating since i can now setup the email as an IMAP account. I currently have a MB Air, MB Pro, iPhone and iPad. I had no issues setting up the two mobile devices as IMAP, but I cannot set up the two laptops. If I set one up as IMAP, the other one's Apple Mail does not work. Or I can switch them, but under no circumsyance can I get them both to work. I would prefer using Apple Mail on both laptops for consistency sake. I have done two online chats with Apple Support, plus an hour-long phone call with Verizon tech support. The Verison person said he has helped other Mac people with no issues; I am the first.

Are there any other Mac people who had this isse and figured out how to fix it? It is making me crazy.