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Once you go to your PM area, you will have a check box that will 1) check one PM or 2) select all for a period or 3) select all you have.
Once you have the ones checked that you want to delete, go to the bottom right of the screen, choose the drop down, and choose delete. Then press the GO button.
If you have "unconfirmed" messages to delete, on the right side of my pic, under the Private Message title, press the Track Messages link. This should show you all messages including unconfirmed.
Then select, choose delete, and GO just like above.