How do I open the door on a coopers 2005 if the batterie is dead

SOURCE: mini cooper key fob settings

Try pushing the unlock button twice.

Mechanic @ Large Mobile Automotive Service Tucson,AZ
www.mechanic-at-large.com

SOURCE: my car key dead on mini cooper 2006. how I change

Should be able to "Pop" case open, case is tightly sealed with o-ring

SOURCE: battery on my mini coopers is completely dead,

pull up the rear seat (the bit you sit on ) , it is held in place with pop fasteners , so just pull it up the way. underneath is a cord with a loop to pull to open the boot catch.

SOURCE: where does the battery go in a 2005 mini cooper s

In the S model it's in the boot under the floor mat.
In the standard model it's under the bonnet on the left sidr of the car (US Drivers side) You'll see the cables going into the plastic battery box.

SOURCE: 2005 mini cooper battery was

Have you looked into the PSP (Power Steering Pump) relay, or the cooling fan? This problem has been know to create issues and lead to a dead battery. For more information, read this forum of MINI owners, there are quite a few with your issue, and they are trying to get a recall. the 2005 MINI's also have a headlight recall.
http://newmini.wordpress.com/2009/02/17/mini-cooper-power-steering-failure/#comment-884