My speedo stopped working on my 300 too. I disconected both ends and hooked a cordless drill to it and spun it awhile. I also noticed that on the end that attaches to the speedometer, the shaft was able to slide down and didn't seem to engage the speedometer very well. At any rate it started working. It was either not turning or was not engaged at the speedometer. I beleive it was the engagment. Try disconnecting at the speedo, pulling the shaft out a little and reconnecting.
I reread your post and realized you said the cable broke. if you say it broke because the speedo stopped working try what I said above. If the cable is broke in two, ahhh never mind :huh:
Both cables have broken the tip off where it connects to the rear differential. You cannot replace the tip, you must replace the cable. I thought that there might be something in the rear end causing it to break.