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All the '41 calcs have four screws, one below each foot. It is quite easy to open and close the '41s. Just be real careful not to overtorque the screws when putting it together again. In particular the upper screw bosses in the case back have a tendency to break because the plastic is quite thin and had become a bit brittle with age (actually HP knew they had a problem here soon after the machines were released). The lower screw posts can also crack off if you get the screws past their limits.
Another problem that occurs is the screw posts split vertically. They can be repaired with styrene melting solvent (plastic welder) available at most good hobby shops (Hobbytown carries it). Brush it onto the outside and inside of the cracks, hold the post together for about a minute, then let it set up overnight.
The circuit card in the fullnut sits on a conductive elstomer strip (zebra connector) and uses the case tension to hold it in contact with the keyboard.
The half nut designs (rounded LCD display corners) have a single chip surface mounted on the keyboard. They do not have the problems associated with the zebra connector system. Their main problem is the the wires to the piezo beeper disk WILL break off if you even think about opening the case. They are rather thin and the solder connections at either end seems to become brittle with age. Expect that you will have to resolder at least one of them. Feel VERY lucky if you don't.
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The first thing to be aware of is that the HP41 is almost entirely MOS circuitry and it _is_ possible to damage it by electrostatic discharge. This damage may not show up at the time, the machine may work when it's put back together and then fail days or months later.
It is important to take anti-static precautions (use a proper earthing wrist strap, work on an ESD-protected bench, and so on).
That said, I take reasonable precautions, and have never zapped an HP41 or any other HP calculator.
All HP41s have 4 screws holding them together. Sometimes the feet peel off and leave the sticky layer behind, hiding the screw head. Try peeling it up to find the screws.
The are 2 basic types of HP41, the original (or 'fullnut') and the halfnut. The easiest way to tell them apart is by looking at the display -- the halfnuts have a black border around the display with rounded corners. The fullnuts don't
To take apart a fullnut, remove the battery pack and the 4 screws. Lift off the bottom case (it comes right off). Lift off the centre case as well (a U-shaped piece of plastic -- make sure you put this back the same way up). Looking at the back of the keyboard, you'll see the logic board (covered with chips) in the front. Lift this off too -- early
machines have a couple of nuts you have to remove first. Then you can see the keyboard. There's a hole (a PCB 'via') under each key. Start by spraying a tiny bit of propan-2-ol into the one under the '2' key. if that doesn't hel
then try the wire-brush trick mentioned elsewhere in this thread. The logic board _and the keyboard PCB (which is connected to the display module) are the static-senstive parts. Clean also the contacts betwene the logic board and the keyboard and the ones between the I/O flexible PCB (in the lower case, connects to the modules and the battery pack) and the keyboard. Then put it all back together again. Do not overtighten the screws. A good trick here is to put them in their holes and turn them 'backwards' (counterclockwise) until the threads engage. Then tighten them. This avoids stripping the threads.
On the halfnut models, again start by removing the battery and the 4 screws. The beeper is mounted in the bottom case on these machines, so there are 2 thin wires joining it to the circuit board. Carefully lift up the bottom case and turn it over towards the left side of the machine. Then remove the centre case as above.
There is one PCB in the halfnut, no separate logic board. Again you can clean the keycontacts as above. On the halfnut CX, there's a PCB soldered to pins across the top of the main chip. I think you can get to the keys without desoldering this. You can certainly squirt them.
There's only one set of contacts (keyboard to I/O flexible PCB) to clean in the halfnuts. Put it back, using the methods I described for the fullnut.