Motherboard type/model? And what does it say exactly on the fan connector you're using with the cooler? I guess this cooler needs additional power from PSU. Check if it's connected.
probably fan cable connected to incorrect place on motherboard if fan won't spin. Might be defect fan and/or broken connector on MB too in theory..
And since it stays on only 20s, I guess CPU isnt touching the cooler at all.
check if cooler is really pushed against CPU and there won't be air flow between cooler and cpu..
and your previous paste should've looked like it's been squeezed between cpu and cooler, right?