The CPU needs 95 watts and the motherboard can only go up to a 95 watt CPU. However, I want to unlock the 4th core in the CPU, and I am worried it will need more power. So if I unlock it will the mobo still be able to handle it?
Unlocking the fourth core will not increase your power consumption to the point it would be a concern to your motherboard. Yes, your motherboard will be able to handle an unlocked Athlon II X3 440.
Even if the core voltage needs to be tweaked to stablize a potential 4th core, the CPU will probably never go above 80-85W in real world situations. Avoid long stress tests, 10 minutes will show stability, and you will be fine.