I recently gutted out an ASUS laptop with a friend of mine, every part is still perfect working condition except his case...
As mentioned, we we're curious of ghetto rigging everything back.
His laptop was powerful enough to run RES:5 No mercy pretty damn well, no lag.
How to put this... would it be possible to restore the beast back into a working condition?
Also, the PSU kinda sucked.
Other than that, as mentioned once more, everything else is still practically perfect.
First things first...
Laptops have transformers/batteries not PSU's
Most laptops I've seen have 16V-24V DC input - if it's 24V, you could buy two PSU's and run them serial. If I have lost you yet, the answer is NO!
The trick would be to find out what power inputs go where on the mobo... or use the original transformer
What exactly are you planning on doing? It will be an arduous task to get everything to work outside of the laptop case itself. You'll have to figure out what the power requirements are, as c12friedman said, and then figure out if it's feasible to even try to rig something up to power it.
Then you have to figure out how to actually turn it on, since there won't just be a button for that, unless you can figure out how to take the power button out of the case and put the leads back in into the correct place on the mobo (if that's even possible, though I suspect that it should be).
In any case, it's a lot or work for something may not even work the way you think it will. Obviously, you'll have to have a monitor hooked up to it, since the LCD from the laptop can no longer be used, as well as a keyboard and mouse because and you won't be able to use the keyboard and touchpad from the laptop.