I know this is bumping up a really old thread, but i found it on a google search as i too have recently misplaced my Boots Advantage card and have just called to request a replacement, and i thought i would just clarify what the 'Dont Post/Mail' thing was all about.
When you registered for your card originally you may have ticked a box saying you didnt want to receive any offers/mailings in the post from Boots, hence the Dont Mail note attached to your account.
The guy just asked me if i wanted that removed from my account, so i said yes, just in case its the reason that the new cards are not being received!
Hope this helps someone else in the future.
And also, if you have an old receipt where you've used your Boots card, it has the number of your card on the bottom, on the right hand side, marked with a star, this is useful if they cant find your name on their system, like in my case!