The keyboard problem is very common with this computer. The keyboard has a carbon membrane that sits between the key mechanism and the keyboard circuit board. There is a replacement manufactured by someone in Europe for around $25. So I went ahead and ordered a new one.
After taking the keyboard apart, I noticed that most of the internal standoffs that the keyboard mechanism screws to had been broken off. In addition, the standoffs that the keyboard connector screws onto had broken. Basically, there was very little holding the keyboard itself inside its shell. I had a sense of this, as the unit seemed to rattle a bit before I took it apart.
I decided to design and 3D print new standoffs for the keyboard socket on the back of the keyboard and for the mounts that hold the keyboard to the bottom half of the housing.
I filed down the remaining standoffs and 3D printed new versions. After a few iterations to get the sizes of the parts exactly correct, I used JB Weld to glue new parts in place. I think the new parts are actually much better than the originals as the originals had become quite brittle.
Since I had all the keycaps removed to get to the membrane, I individually cleaned all the keycaps with soap and water. The spacebar was pretty yellowed from UV light exposure. Interestingly, it seems that the space bar on a significant number of old computer systems I have restored seems to be made from a different plastic than the other keycaps and is often more yellowed than the other keycaps.
To correct the space bar color, I placed the space bar in Hydrogen Peroxide and placed it under a blacklight for 6 hours, and it returned to its normal color. I left all the keycaps on the kitchen counter overnight to dry. This turned out to be a mistake, as the next morning one of my Labrador Retrievers had retrieved the spacebar from the counter and was carrying it around quite proud of herself. Thankfully, only minor scars were present.
I developed a rule for myself a few years ago after other keyboard incidents. You only keep the caps off the keyboard for the absolute minimal time to prevent entropy accidents like this. Other times I've lost a key in the dishwasher and another in the garbage disposal. The sooner you figure out it's missing, the better!
Once I received the membrane, I reassembled the keyboard, and it worked flawlessly and looked like new (except for the small nick in the spacebar).
Link to the Keyboard Membrane replacement I used
Link to the STL file for the front keyboard standoffs I designed
Link to the STL file for the keyboard cable bracket I designed