Only one key is acting like it is sticking (w key)

I have an about 4 years old macbook pro (Mid-2012 A1278 model) and the W key has started acting glitchy. It will behave like a sticky key for a few seconds after pressing, holding and releasing the key, and if I play around with the key (repeatedly tap, press and hold, etc) the key will even "press" a few times after acting like a sticky key. However, if I use the key normally (eg. typing out this question) the key will behave normally. It is only during repeated tapping and holding the key will glitch out.

This is really annoying and has really hindered my ability to play games (especially first person), forcing me to play only arrow key and point-n-click based games. I have noticed I can cancel out the stuck key by pressing another key while it is behaving like it is stuck, however it only works for the duration while it is acting stuck. If I release the key while it is still stuck, it will continue to input the w key. If I continue to press and hold another key until the w key stops being "stuck", the other key will then input (eg. press and hold S, it won't input S until the W key stops being stuck).

Here is an example output from the key will pressing and holding:

(the bolded are inputted after releasing the key)

wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

(Tapping the key now):

wwwwwwwwwwwwwwwwwwwwwwwwwwwwww

I know the keyboard is the problem as I have tested with an external Logitech keyboard and the key works fine. Because of that, I am thinking of buying a replacement keyboard (no topcase) online and replacing it myself.

On a related note, how fragile is the keyboard backlight sheet in the A1278 models?