I see this post is a bit old, but it just came up as a google search, so why not. I've done this a couple times now for cleaning and RAM upgrades (I have my old zt1135 up to 1GB! Got a strange "Unexpected amount of memory" error...funny). There is certainly a trick to it, but it is actually quite fast and simple once you figure it out.
First, forget all the screws on the bottom, the best way to access the mobo is from the top (unless you are replacing the mobo itself...in which case I've got nothing for ya). Start by removing the two screws on the back of the case (near the I/O ports) that screw into the pivots for the screen.
With these out, you can pop out the panel that has the power switch, speaker grilles, etc. Works best the fold the screen all the way out, then gently pry on the inside of each cover of the pivots. Sort of work your way around, and keep in mind there is a PCB on the back side of it to mount all the HP one touch keys, and also a fairly short wire connector off the back of it.
Once you have the speaker grill/switch panel off, you can get to the 3 screws along the top of the keyboard that hold the keyboard in. Remove these, and then the keyboard should pop right out. At this point you can access pretty much everything of interest on the mobo.