Have you switched your isp recently?
Generally, ISPs will only let their users use their SMTP server, which is the server that looks after outgoing messages. They are not so fussy about incoming mail (the POP server), which is why you are still receiving mail to both accounts.
I would guess that your ISP is wanadoo cos you can send emails from this account. In OE, select tools and then accounts and select properties for the wanadoo account. Click the servers tab and look at the outgoing mail box. Note down the contents of the box and any other check boxes that set. One particular thing to look for is if the 'My server requires authentication' box is ticked. If so, you will need to have your wanadoo username and password handy too.
Now, you want to select the properties for the yahoo account and again click the servers tab. Change the smtp server to the one you noted down above. Click the server authentication box, if required, and click the settings button. Select 'logon using' and enter the username and password of the wanadoo account.
Click the general tab and under reply address, type in your yahoo email address. This is so that replies come back to the yahoo account rather than the wanadoo one (cos we are borrowing the wanadoo smtp server and replies will come here by default).
That should be it. You should now be able to send and receive.
(Any warranties expire immediately after reading this
)