Whether it is worth saving totally depends on what it will cost to fix it, and what you are willing to spend on it.
Keep in mind with software, if it is on the OSX side, that you can use migration assistant. I am not a fan of Apple hardware or software, but this is where Apple shines. The best feature of Apple's operating system is the ability to seamlessly migrate applications, settings, software, and more. Simply take your drive out of the machine, plug it into a SATA enclosure, then plug it into another machine. Go to go, applications, migration assistant, and you can copy everything over. This process is made smoother if the new machine has the same OS as the old machine. Mavericks in particular is very picky about what it migrates, you'll get that 157 KB to migrate nonsense where it is telling you it sees nothing. Other versions of the OS do not do this.
In terms of the motherboard status. It "went." Went where? Bad LVDS MUX? Bad MCP? Or just a basic power circuit issue? One way to find out. Are you willing to give more information on the problem? Explain what it is doing, what its behavior is, if there is any behavior at all. Tell us if you have the time or inclination to open it up, go measuring, etc.
Also find the people who put a penny on the GPU and beat them within an inch of their life. They give this entire craft a bad name through implementation of ignorant asinine solutions. I think you mean a copper shiv though. Not a penny. A penny would not have fit. This is still a retarded solution because the heatsink is not the issue, the $@$*!& thermal paste, tiny fans, and lack of intake vents are. The heatsink itself makes perfect contact with the CPU & GPU.