cooling problems

[L.G.]

Hi again,
I recently had a problem with the cooling, sure you guys can help me. Now until several days ago the car was normal, the fan would turn on at the 3/4 of the heat "thing" (:-) ) and cool the engine until the 2/4 point. To see if there was enough coolant I opened the coolant tank cap and then things went wrong. I changed the coolant, because it seems i had left it there for quite some time, after I closed the cap and ran the engine steam started coming out of the cap and at higher temperatures water leaked from the cap. Now it seems ok, the cap is broken (somehow) but it doesn't end there. The fan which used to cool the engine perfectly now can't. The fan kicks in at 3/4 but the temp. goes up! If you step on the accelerator keep it at 3000 rpm in neutral (standing still) then it cools down. Can this happen because of the cap only?
Thanks for reading, answering...