First, as noted, this sequence is for my Pavillion zt1175 laptop. Before I started my repair work, I found a copy of the HP technical manual for the unit - the one "end users" aren't supposed to have. It provides illustrated instructions for removal and replacement of the inverter. You can grab a copy, in PDF format, at either of these locations:

http://www.wir-sind.org/poeschl/xt1000/xt1000_tech_manual.pdf   or 
http://www.martini-man.com/pub/Manuals/zin4.5SvcMnl.pdf

The particular instructions you'll need are the ones that describe removal of the keyboard cover and removal of the display unit on pages 2-9 through 2-10, and 2-20 through 2-21. Take special note that the instructions advise the AC adapter and battery pack be removed during the repair, which makes good sense. Additionally, the replacement inverter for my zt1175 is HP part number F3398-60916, and was available from the HP Parts website for $23 plus shipping. Some 15" zt1000-series laptops take a different inverter; it goes without saying you should verify the one required for your laptop. But I said it anyway. 

Beyond that, all I needed was a small, #0 Phillips-head screwdriver and a nice workspace where I could spread out the pieces. There were lots of very small screws and screw covers to remove, so I set out a paper cup to hold them rather than risk them getting lost on the floor :)

Lastly, the byword in these steps is patience. There are small screws, small connectors, snap fittings, and other seemignly tenuous things that can and will break if proper care is not exercised. Including the time it took to take pictures (and read my nightly Bible verses to my 7-year-old assistant), it took me about 45 minutes to complete this project.