Possible CPU and power supply issue!

Hello everyone!
I am new to these forums, so please bare with me.
Well for starters I have an HP s5310f (nothing fancy) and I have been wanting to push it to it's limits, by that I mean adding a GPU (Radeon HD 5570- probably the best one for a slim tower like mine) and replacing the stock AMD Athlon II X2 250 w/ a AMD Phenom II X4 840. So far so good but I wanted to know if my 250 watt powersupply will do the job for a while? Also, I did not use the CPU fan/heatsink that came in the processor box because my motherboard only has a three prong CPU fan connector and the one that came in the box had four. I figured it would still work so I plugged it in and I received an error telling me that my fan had failed, although it was running just fine. Anyway, after that I decided to use the fan that came installed with the old processor and it worked just fine, but my question is, would that thermal paste leftover on the old heat sync be sufficient enough?