If the molten core solidified, would the earth stop rotating on it's axis?

yes

The solar system condensed from a huge rotating disc of gas and dust. Almost everything that was formed from that disc still rotates billions of years later, and also revolves around the Sun in the same direction as the original rotation. In many cases the rotation has slowed down due to tidal forces, such as Mercury's rotation which is now tidally locked to the Sun so its day is the same length as its year. The Earth's rotation has been slowed due to tidal forces from our Moon - back in dinosaur times the moon was much closer, and months and days were shorter. Celestial bodies in our solar system have also had their rotation altered due to collisions. Originally all the planets had their axes aligned parallel to each other (and to the Sun's axis), but Uranus got hit by something huge a long time ago and its axis is now tilted over nearly 90 degrees. Earth had something similar happen; our axis is tilted 23.5 degrees which is why we have seasons. If the Earth's core solidified it would keep rotating like nothing happened.

I dont know if the earth would stop spinning, I doubt it though. I do know that the elctromagnetic feild surronding the earth and blocking out ultaviolet waves would shut down, leaving the earth and its creatures open to massive radiation damage

The earth's rotation is not dependant on it having a molten core and is dependant only on the electromagnetic pull of the sun on the earth.

It would slow tremendously, but not stop. Cetrifugal Force

it would mess everything up, thats for sure..if the earth was a big cold hunk of rock- then lots of natural cycles would simply stop