Does the machine still run on the battery? If so then I'd suggest you might be better off getting a replacement psu.
Not knowing the circuit I could not comment further. I had a dell go down, reason? Damaged cable from the psu to the laptop, it could be seen where it had melted near the power plug on the computer itself, I imagine psus do not like a sudden short across their output and something will give. However you need to get yourself a meter and check a few things. If I could see, I'd probably first decide if its a switch mode or not. The give away is that it will have a tiny transformer, but if its analogue then it will have a big heavy one. If its a switch mode then, personally I'd not mess with it any more its knackered. However if its an analogue, which these days is unlikely, take out the bridge and see if there is ac volts on the transformer secondary, Put a battery across the bridge in either direction, and measure the volts on the other two legs, It should be the same polarity no matter which way around the battery is placed. If it is not then the bridge is dead. Then you need to figure out what the circuit itself after that does. Very old psus were simply a smoothing capacitor and that was it, but I suspect there is at the very least some kind of regulator in there.
From your description though my feeling is that its fried quite a lot of stuff. You need a manual. As though, I suspect a switch mode, mostly these are bin it jobs. Brian