My speakers are 20 years old and until today I thought they were going
strong. I have always known that they sound better with the grills off,
but because the drivers are made with polypropelene I have always
assumed that I should mostly keep them on to protect them from UV. Every
once in a while I take the grills off and today I did so. For whatever
reason I decided to touch the tweeter dome and was surprised that I
could not feel any vibration at all. I turned the treble knob to full
and tried changing CDs but I could never feel the tweeter dome move at
all, this was on both speakers. Am I supposed to feel the tweeter dome
move?

You're worried about UV, but put your sweaty fingers on them? :-)

See those funny-shaped things each side of your head? They're called
"ears". Put one near the tweeter. Hear anything?