Chosen Solution
I just got a my first 1998 furby in the mail. I put batteries and it took a few minutes before she turned on. I noticed that she doesn’t recognize that I’m petting/tickling her. She knows when i press her tongue and move her around, but not when I pet her. Is there any way to fix this, preferably without taking her apart, or will she just be like this forever?
There is a simple metal contact switch in the back. See this video for the specific location. https://youtu.be/fNaNM4_fKTo?t=71 See if it is dirty, corroded, or just plain bent. You might need to rig something up to replace it if something is seriously wrong with it.
Also, I would like to add to what Isaac said, If the furby does not recognize your tickling her then the metal contact on the speaker in the front is dirty, corroded or bent. You can replace this mechanism, with another similar furbys speaker/touch sensor.
Hope this helps!