I thought all LS models had a digital clock.
For the needle to be stuck at a certain speed like that makes me think something is off in the speedometer. My understanding is the speedometer should read "0" unless it's getting a signal from the speedometer cable. Does the speedometer work above 35 mi/hr?
I just noticed this weekend my speedometer is bouncing at lower speeds. I don't recall it doing this before so maybe it's a function of the higher ambient temperatures we've had lately. Either way, it appears the signal being generated by the cable is being disrupted somehow.