HEF4060B counter doesn't count
Be aware that breadboard connections can have a LOT of capacitance. The Wikipedia Page on them states 2-25 pF per contact point, so you may have far too much capacitance on your crystal.:


  Due to large stray capacitance (from 2-25 pF per contact point), high inductance of some connections and a relatively high and not very reproducible contact resistance, solderless breadboards are limited to operation at relatively low frequencies, usually less than 10 MHz, depending on the nature of the circuit. The relative high contact resistance can already be a problem for DC and very low frequency circuits. Solderless breadboards are further limited by their voltage and current ratings.


Another link from an Illinois ECE college course states: 


  2) There is generally a 10pF capacitance between rows on a breadboard. This is negligible for most frequencies, but if you are operating in the RF spectrum this quickly becomes problematic. This is generally why high frequency devices avoid breadboards. You could try to separate components on the breadboard, but this increases lead inductance in the connecting wires which have to be longer. Use PCBs for anything in the RF domain.


Basically, the intrinsic capacitance of the breadboard may already be equivalent to the needed crystal load caps. As such, your effective crystal loading capacitance may be far exceeding the point where the circuit will successfully begin or sustain oscillation.



If you can, I would strongly suggest lifting the two crystal pins (bend the leads on the DIP package up, so they poke out of the device horizontally), and soldering the crystal and caps directly to them. This removes the breadboard from the connection entirely, and will likely be far more reliable. However, it would make changing the crystal somewhat more involved.