Magsafe DC-in, water damage or something else causing no/slow charge?

Considering the fact that your Mac turns on, I don't think that the logic board is fried. iFixit provides tools, guides and parts describing how to fix your MacBook. The battery may have suffered eternal damage. Because you have a sealed lithium-ion battery, any temporary short can cause problems with the battery. Use a Phillips #00 screwdriver to remove the bottom cover. Use a spudger (search the iFixit store if you don't have one. Make sure to use the static-safe spudger) to remove the battery connector (this connector is very fragile, so be careful!), then use an iOpener (it looks like a long bag from iFixit) to loosen the adhesive that holds the battery into place. Carefully look at the battery. Is there any liquid damage or are any of the battery cells bulging? If so, this is bad. Don't put the battery back in. Instead, order a new battery (again, iFixit has batteries galore). DO NOT THROW THE OLD BATTERY IN THE TRASH!!! This is environmentally irresponsible, not to mention incredibly dangerous. Take the battery to an electronics recycling center. Check with your local electronics stores to see if they take lithium-ion batteries. Next, take out the logic board and remove as many components from the device as possible. There are many different types of screws. You're going to need several unique bits, including the Apple Pentalobe and the triwing bit (iFixit has all of these). Use the Magnetic Project Mat (available from iFixit) to keep track of the copious number of screws. Take lots of pictures, so that you know how to put your Mac back together. Examine the front and back of the logic board. Bulging capacitors and resistors are bad, and you want to avoid touching them. If there are bulging capacitors or resistors, then you may as well declare your Mac dead. I hope this helps.