Logic-Boards are expensive, so first you should try to fix them, if the board itself is short, then you pretty much cant do anything about it and you would have to replace the Logic-board. The reason Logic-Boards stop working could be due to Liquid Damage, GPU and MCP Problems, or overheating due to dust and moist. There could be a small fuse burnt, or there could be a big chipset damaged. It comes down to the knowledge and experience of the technician working on your device and how lucky you are.
If you could get a free diagnostics from any of the stores around you, you should, because then you will probably save a lot of money. If you are in a hurry to get your device fixed ASAP and do not care about the money or if your board is fully dead and its not fixable, then replacing is an option. Best prices are always on Ebay. Sometimes some Macbook Repair Stores in Toronto offer better prices.
Bottom of the line is that, there is always a solution to all mac problems. It’s a game of luck and money. You should take your mac to a shop that you trust. Read the reviews online and get an idea of how they could help you.