Paul, I remember this one... came up last year when Don Wallace was fielding repair questions. When there was a thread left to read what didn't come out was what you just posted - that the unit "takes absolutely ages to respond". That's the smoking gun as they say in Hollywood... With that info in hand, here's my take on the problem:
Opening the case isn't going to help :(
The problem is inside the shift key and that is... very ugly. Bottom line is the key is leaking electrically. Only needs to be several megohms and you've got a slow machine - as the keyboard is hung across the processor's data and address bus - and the Saturn doesn't like the leakage.
You could try washing it out in an ultrasonic cleaner. If you have access to one, use three cycles of distilled water, shake it out after each cycle and leave to dry in a warm place. That might clear it, just depends on whats inside.
Another trick - since I think we can assume it is the shift key - you can try to flush it out directly. With batteries out, direct several drops of isopropyl alcohol directly around the left shift key. Press the key several times, hold unit sideways so lcd is on the left, shift key at the bottom so the gunk drains away from the rest of the keyboard. Repeat several times. Let dry well - a couple of hours is a good idea before the batteries go back in. That might get it going - but again, depending what is inside, the problem may return.
Now for the disclaimer: DO NOT use contact cleaners - anything with silicone is a keyboard death sentence.
Edited: 17 May 2006, 12:03 a.m.
In case anyone is interested, here's how to open your HP48