Update 2010-04-06: Looking at the stats, a few people are finding this page through a few search engines. I've polished the page a little to make the pictures more useful, and enabled comments in case someone has a question.
I dug up my old HP49G to help me do taxes this year. After probably a year of not using it, the on/off/cancel button was almost completely unresponsive. After poking around on the web, I found some directions on safely pulling the case apart, and decided to give it a shot. I shot some pictures of the process, and some close-ups of the problem causing the power button to fail.
Here are the basic steps I followed to pull it apart:
1. Drill out the heat stakes in the battery compartment. I had a decent 5/32" drill bit on a quick-release shank that made it really easy to remove the stakes by hand.
2. Pry the case apart. I used the handle of a plastic spoon to keep from messing up the case. Some care was needed to keep from breaking the tabs at the top of the case, and to free the battery terminal from the back of the case.
3. With some small needle-nose pliers, carefully untwist the six metal tabs above and below the area of the circuit board connecting to the display. Pay very careful attention to the direction they were twisted into place and reverse them. It will take some coaxing to get each tab to line up with the slot in the circuit board. Take your time.
4. Carefully pry the circuit board away from the front of the case.
At this point, you have access to most of the parts that can cause problems (especially with the keyboard and display). All I had to do was reposition the foam pad below the keyboard's connector to make sure it supported both ends of the connector. While I was in there, I cleaned up all the contacts with isopropyl alcohol and carefully blew out the recesses with some canned air. After reassembly, the calculator powered up perfectly, and the on/off/cancel button has never failed to work yet.
Click any of the pictures to see the ultra-huge version. (Courtesy my Canon Elph SD1100 [a few shots in macro mode].)