How would I do this? What sort of screwdriver would I need to open the ones along the edge on the back (in the deeper cavities).

I'm pretty sure I need a Torx screwdriver, but what size?

And after getting the back open, how would I further disassemble it?

The screen is broken. Turning it on, it would appear the calculator is still off - in actuality, the calculator IS on, it's just that nothing displays. I figured out the calculator is actually on because when pressing the "y=" button, I get this on my screen:



(There a few dead pixels on the side, but that is merely a minor inconvenience).

An excellent and easily-answered set of questions:
1) You need a Torx-6 screwdriver for the six Torx screws
2) You need a Phillips screwdriver for the backup battery.
3) You can also use the Phillips screwdriver to remove the two screws holding on the antistatic shield, but you can replace/repair the ribbon cable without removing the shield.

To actually get the two halves of the case apart, you must first trip the latch at the top of the case, then lever the two halves sideways to each other. More information on the actual repair process: http://www.cemetech.net/forum/viewtopic.php?t=5161

Thanks Kerm for that simple, yet quite useful information!

I'll have to buy the Torx screwdriver, then I should be set.
I hope repair is possible, and if not, it'll at least be an interesting experience.

It's definitely possible from the symptoms in that image, which exhibits classic coarse-grained ribbon failure. However, it takes some fairly finicky soldering to repair, especially if you're not used to doing fine-pitched soldering.

I found that a small flathead screwdriver is just fine for those pesky 5-pointed screws.

Six-pointed Torx-6, actually. And yes, you need just the right side flathead screwdriver, but it works. I just used that trick on my new calculator, as a matter of fact!

Torx T6 if we're being pedantic. Lots of small electronics use Torx screws so it's definitely worth picking up a set.

Definitely agreed on this. I bought mine January 1st, 2000, and I have used it on hundreds of devices since then.