Test works fine, but message truely not being sent

Our business recently purchased email accounts from Yahoo. When setting up Outlook 2002 to check our accounts, Outlook seems to work properly when using the "test" feature. But outgoing mail is truely not being sent although it says it is. Passwords, etc have been triple checked and mail appears in Sent Box. Everything says the communication is correct but emails are never delivered. Mail is however reveived using Outlook. AOL is used as our primary connection but we realize we cannot use Outlook to check AOL mail. We simply want to check our business (POP3) email. Any ideas?
Thank you in advance.