Hi David, some previous discussion on different groove making techniques here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3859.2

But yes if you have a surface rather than a solid as your base object, then as others mention above you will probably need to use Trim to do the cutting up of pieces rather than booleans.

Booleans are more oriented towards working with solids and they figure out which pieces to keep and which pieces to discard depending on which volume the particular pieces are contained within.

If you're trying to cut an open surface rather than a solid the booleans won't really be able to use that same volume containment mechanism to do their work. So instead you can use Edit > Trim - trim cuts up the surfaces of objects and lets you manually pick which cut up pieces to discard or keep, it's usually what you would use when doing surface modeling rather than working with solids.

The booleans kind of work like a "high level" version of Trim + auto selecting pieces to discard + join at the end. Since they bundle up several steps of work they can be convenient but they are meant to work with solids. Sometimes it can be good to form your base object into a closed solid before doing further work on it so that you can more easily use these kind of "batch" operations that the booleans will do.

If you are still stuck could you please post the 3DM model file with your battery compartment door in it that you're trying to work with? It usually helps a lot to be able to see the actual model example that you are referring to rather than just a written description or just a screenshot.

- Michael