To open the calculator, you first need to pry up the plastic screen guard. There is a video of this on youtube.
Here is one such link.
Once you have the screen guard off, you will then need to be careful with how you open it. After removing to screws at the top, you should be able to simply pry the two halves apart with your hands. (This is actually hard to do, but with a LOT of patience, it will separate.) Do NOT pull the halves apart too quickly as the speaker wire connects the two halves. You can pry the speaker apart (it's merely glued to the battery half) and then safely separate the two halves.
Once you have completed this, unscrew the mini screws and also cut through the plastic rivets that hold the PCB to the keyboard. What I did was simply drill away at the top with a hand drill and this was enough to defeat the rivets yet still leave enough of it to use the screws to keep the PCB in place.
What has likely happened is that the "peg" underneath the [3] key got bent, broken, worn, etc. Or, the metal dome has gone kaputz. If, however, the problem is that the key's "hinge" has broken, you can probably fix it with some flexible epoxy. You may as well throw on an epoxy layer for the other keys while you're at it to prevent future problems. If you look at the photos, you can see how poorl even the most current keyboard design is. The little pegs underneath each key are simply to thin/small and their strength is easily compromised from normal usage. (Those pegs are at least 4 times as thick on the HP48 series) Moreover, the keys nearly puncture through the thin layer of rubber foam that is used to give the keys a soft feel upon pressing them.
Here are some photos which you may find useful:
Photo 1
Photo 2
Photo 3
Photo 4
Photo 5
The photos won't be up for long.
Edited: 13 Sept 2010, 5:26 p.m.