If the power supply is ATX 2.0 compliant, then it should be enough.
BUT...most power supplies that come with cases, from what I've seen, aren't ATX 2.0 compliant. There's an easy way to tell, though - an ATX 2.0 power supply has a 24-pin plug that it uses to plug into the motherboard and an older one has only 20 pins. Look at the big plug on the power supply that's plugged into the motherboard and count the pins - it's that simple.
If it's a 20-pin instead of a 24-pin you could try to plug it in anyway on your new board and hope for the best. Some people have done that and reported success, but others have reported that it didn't work. I wouldn't recommend it, though, because I don't think taking the chance would be worth it. Shoot for getting a nice ATX 2.0 power supply like the one I suggested if the one you have doesn't have the 24 pins.
Having a quality power supply in your computer is extremely important, and it's something that people looking to buy a computer tend to overlook. Make no mistake about it - a bad or insufficient power supply can cause all sorts of headaches for you.