Yep, some up and down play is normal between the lower and upper sections of the shaft.
Just off the top this sounds like a bad ignition box. (if we are ignoring a possible chain jump for the moment)
Disconnect the plug that goes to the distributor and with the ignition on touch the exposed metal bullet on the harness end to the engine block to ground it.
Each time you touch it to ground you should get a good spark.