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Delete messages that are in your 'sent' folder and 'delete' folder. It's not only inbox messages that take space - sent, deleted and drafts also take up space. Tell me if it works once you have done this.
 
I delete my sent messages

How do I receive my stored messages? (2 stored, all other folders empty)
If you still have 2 stored messages, that means that not all folders are empty.

After clicking on 'settings' in the top right of the screen you can check your PM folders. These are on the left side of the screen under 'My messages'.

Click each folder: it will probably state something like the following:
Sent Items contains 0 messages. You have 2 messages stored, of a total 2 allowed. (Empty Folder)
This means there are no messages in the Sent items folder, but there are 2 stored messages in a different folder somewhere. However if it says:
Sent Items contains 2 messages. You have 2 messages stored, of a total 2 allowed. (Empty Folder)
This means there are 2 messages in your Sent items folder and you have to delete them to clear space for new messages.

Check all your folders until you find the folder where the messages are stored.
 
If you still have 2 stored messages, that means that not all folders are empty.

After clicking on 'settings' in the top right of the screen you can check your PM folders. These are on the left side of the screen under 'My messages'.

Click each folder: it will probably state something like the following:

This means there are no messages in the Sent items folder, but there are 2 stored messages in a different folder somewhere. However if it says:

This means there are 2 messages in your Sent items folder and you have to delete them to clear space for new messages.

Check all your folders until you find the folder where the messages are stored.

My INBOX has Inbox contains 0 messages. You have 0 messages stored, of a total 2 allowed. (Empty Folder)
My SentItems has Inbox contains 0 messages. You have 0 messages stored, of a total 2 allowed. (Empty Folder)

However, in my email it says
"Dear CattBoy,

MagicManICT has just tried to send you a private message. However, your private messages box on Paradox Interactive Forums has reached the specified quota. In order to receive further private messages, you must delete some messages. Please visit this page to do so:
http://forum.paradoxplaza.com/forum/private.php"

Now, I am asking how do I receive these messages (from the email notification) or were they never sent in the first place since my box was full?
 
OK, now it says "0 stored", previously it said "2 stored". So you should now be clear to receive any new PMs.
 
The answer to your question is you cannot.
You would need to contact him and ask him to resend it.
You are very close to a bump in PM limit, that limit is only for very new members.