I have seen this problem once before with a Laptop I fixed. The problem was a loose screw causing the motherboard to short out when jarred. Has your computer ever been opened or worked on? Is it a laptop or a Desktop?
I cleaned the board several times and found a tiny metal fiber (from what, I cannot say) laying across several IC's. Removed it and it boots up fine. Just goes to show you kids, it's not always a backlight coil ;)
I'm sorry I haven't gotten to it until now. But yes, it is worth trying to fix. I recommend removing the Logic Board and placing it in a sonic jewelry cleaner filled with 100% fuel grade alcohol and running it for 30 minutes with the heat on low. I have fixed countless water-damaged phones with this method.
There is no antenna in the battery of your phone. Do not attempt to disassemble your battery if you do not know how it works; it would likely end poorly. Poor signal could be due to the building you are in, and/ or the coverage of your carrier. Who is your carrier? Have you attempted to look at their coverage map to see if the problem lies in the coverage?