In Tools -> E-mail Accounts -> Internet E-mail Settings make sure that you
provided correct server information for incoming (POP) and outgoing (SMTP)
mail servers.
In Tools -> Send/Receive -> Send/Receive Settings -> Define Send/Receive
Groups include the accounts you want to receive and send e mails using the
New or Edit buttons.
Also check your contacts in your address book for correct e mail address
entries and in which categories you chose them to be.