Keyboard backlight not working

Your uppercase holds the keyboard and just behind it is the keyboard backlight and its light defuser which lights up the keyboards keycaps. What likely happened is something spilled into the keyboard and dripped through the openings wetting the keyboard backlight assembly corroding it.

Luckily its not too hard to get to the keyboard backlight assembly you’ll need to remove the logic board and a few other parts following this guide MacBook Pro 15" Unibody Mid 2012 Upper Case Replacement some parts which are not directly over the keyboard area can be left in place.

Here’s a 2009 model which is the same only the power connector is located in a different place

Finding the backlight alone is quite hard as they are part of the keyboard as a set. And given the fact you likely had a spill the keyboard its self is likely to fail soon as well. At this point it just makes sense to replace the keyboard and the backlight together Odyson - Keyboard Backlight (US English) Replacement for MacBook Pro 15" Unibody A1286 (2009, 2010, 2011, 2012)

To get the keyboard out you’ll need to take off about 80 screws! But with a small power screw driver it will be less work and save your wrist!

Here’s the info for your second problem!

You have a damaged Inductor L5850 which is 10UH 0.58A / 350 Ohm, part ID 1098AS-SM

You’ll need to talk to talk with TDK or other inductor maker to find a source I couldn’t find it in Mouser. The only other option is finding a junker systems to salvage the part.