Jig highly unlikely to work (1/10,000 chance, and I'm being generous), but try one as you have nothing to lose.
You won't be extracting data from the device, nor will a Samsung service centre or mobile repair shop. The only very very slim chance of getting data off the device would be a company that does data recovery from dead HDD's, but that's the same chance as the jig working - in 2.5 yrs here I've never seen anyone post & say they've had this done. And even if it is possible, expect it to be very expensive (as much as the phone costs).
If you didn't back your data up, it's gone.
If you intend to keep the phone, the fix is motherboard replacement.
If it's important enough to cause you grief if it's lost, back it up. No excuses
Trolling for thanks is lame
Does Samsung's auto-brightness implementation crap drive you to self-harm ? A solution !
Failure to search is the leading cause of male impotence on XDA
If you don't know how to recover if things go wrong, what are you doing flashing custom roms ?