How to repair the logic board on an iPod?

I botched a repair.

Although I’m not a professional device-repair-person, I do a lot of my own repairs; Nothing major, just a few screen replacements here and there. This time, while doing a simple screen repair on my iPod touch, I ran into a battery-drain problem. When plugged in, the screen kept flickering between the apple logo and blackness (It was still able to go into iTunes backup mode though), so I took it upon myself to check every single piece of technology inside the iPod - even the logic board. My prodding tool (a tiny metal screwdriver. I know, very dumb mistake) slipped and touched a small group of connectors on the logic board. There was a spark and a puff of smoke and that was it. Now the iPod won’t even show the apple logo anymore, just a black screen, and anytime it’s plugged in the logic board overheats within minutes.

The point is: Is there any hope of repairing the logic board just enough to get it back on and initiate iTunes Backup? I know the device is now beyond full repair but if there’s any chance of recovering any of the data, it’s worth a shot.