Thanks for using Just Answer.
Remove the valet key from your remote. The chrome cap will snap to one side by pushing it (I believe left with remote facing you). Once it snaps then lift it off. You can now see the parting line for the key fob - pop them apart and you will find the battery.
Yes the car battery can be dead and no on the trunk. Remove your valet key and on the drivers door handle you can remove the cap where the lock cylinder would be. You can then unlock it using the valet key. The key is not a pry bar so use something else to pop the cap off.