You would need at least one stick of ram in. Since the only other new thing introduced to your pc since the problem started is the cooler, try backing off the screws a little bit on the cooling plate on the cpu. Sometimes screwing the cooling plate down too much on the cpu causes the cpu to short itself. Try easing it back a bit and see if it will boot up. Or if you want to try with it removed to see if it will boot up. But of course you will have to reapply the paste and put it back together.
That was my next point of call to do tonight - i've been very conscious not to overtighten the screws when fitting the cooler as instructed on the Manual. Annoying i will have to take off but oh well! After this step and putting everything back to stock and if it's still not working - is there anything further you would recommend? (ie looking at Bios etc?)