About two years ago on my 93 loyale when I was messing with the heater hoses I accidentally yanked on the speedometer cable and the speedometer stopped working.

 

I reattached the cable from underneath the dash, but the speedometer still didn't work. It made a clicking sound that was correlated with how fast the car was going (going faster = faster clicking). What does this say about the cable?

Either you broke the cable, or you didn't plug it back into the cluster all the way.