It depends on the battery chemistry, and the actual model of battery. Typical laptop batteries might only be good for a 2 or 3 C rate. The C-rate is a proportion of how much current you are drawing compared to the capacity of the battery. If you have a typical 2.3 amp-hour lithium cell, that means you can only safely get 4.6 to 6.9 amps out of it before you run into problems of safety, overheating, and damage to the battery.
The newer chemistry and construction of the A123 lithium-iron nanophosphate batteries used in the 36 volt DeWalt cordless drills is very promising. Their specification sheet states that they can safely deliver a sustained 70 amps, and a short burst of up to 120 amps. The battery management circuit prevents you from using the full potential of these cordless drill packs, but if you can get your hands on the cells and build up a pack, you could get pretty close to what you're asking for.
One of those cells can put out approximately 4.6 amps for half an hour at 3.3 volts, and weighs 70 grams. That's an energy of 15.2 watt-hours, and you'd need 40 such cells in a pack to provide 600 watts for half an hour. That pack would weigh 2.8 kg before any packaging or wiring.
In retrospect upon spelling all of this out, unless you'd need the pack to occasionally double or triple its power, regular laptop cells would safely give you that discharge rate. I tend to work more with electric vehicles, and those loads tend to peak a lot higher during hills and acceleration than the nominal.
Lithium polymer might give you slightly better energy per weight.