I presume we're talking about an I9100 ?
The repair shop you took it to is probably wrong/doesn't know what they're talking about; think about it, if something was 'burnt out' on the motherboard, the phone wouldn't boot at all. However, with that said, it is possible the NAND could be corrupted, which is sometimes the case with these.
Find Hopper8'd 'Odin troubleshooting' thread stickied in General & try everything in that thread as many times as you have patience for/until you get a successful Odin flash, these cases are always fixed with persistence when they're actually recoverable (which is often the case when you still have download mode).
If you find after days of trying you can't get a successful flash, take it to another mobile repair shop. Most likely fix will be motherboard replacement as it's not feasible to just replace the NAND (very fiddly to do & would cost you more in labour than a motherboard replacement).