My 04 XLR trunk opens when you push the FOB or inside button. Closes when you hit the close button inside the trunk lid.
Sounds like a strange problem. Check to make sure the Valet Lockout switch is in the OFF position.
I don't have the 05 owners Manual but you may want to verify it's operation.
The 06 XLR manual is downloadable from the Cadillac site.[2004, 2005 are not on there , too old I guess]