Every laptop PSU I have ever seen outputs in only a single voltage. For example my laptop PSU outputs at 19V 4.7A.
The A1200 requires +12v, -12v, +5v and ground. This means you would have to build some extra ciruit to step down the initial 19V and create the three different voltages required. (I have no idea how to design that sort of stuff, but I could probably build one from somebody else's design). :-)
In short, it's not just a case of attaching the A1200 power connector to the Laptop PSU, theres more involved than that.