Answer to: Spill on MacBook ProWhen liquid is spilled inside a MacBook you will often find yourself replacing several parts including the Logic Board. If it was potable water (regular old drinking water) you can often get away replacing fewer parts (usually logic board.) I would forget about repairing it if you spilled just about anything else including soda, coffee or another "sugary" liquid which usually corrode all sorts of important things inside the laptop.
Answer to: Diagnosing why this LCD screen has sections brighterWithout physical damage to the LCD/Display, this is often caused by a faulty LVDS (display cable.) What happens is the hinge wears through the display cable over time and shorts it out causing issues like this. The only downside to resolving this issue is that unless you replace the entire display assembly you will have to completely dismantle the display and open up the computer which is quite a task on these MacBook Pros.
Answer to: Problems with powering system - Battery?You should try resetting the SMC (System Management Controller) To reset the SMC: Shut down the computer. Plug in the MagSafe or USB-C power adapter to a power source and to your computer. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time. Release all the keys and the power button at the same time. Press the power button to turn on the computer. On MagSafe power adapters, the LED might change states or temporarily turn off when you reset the SMC.