Wow, this actually worked! I paid c.£200 for a similar repair a few years ago and wasn't willing to spend the same again on my ancient macbook, so figured I'd give this a try.
Opening up the inside was pretty scary and I fully expected to do more damage than good. In fact, my first attempt produced a blue screen with a question mark icon, so I repeated steps 1-18 to check for a loose connection/trapped cable and, much to my amazement, that fixed the problem! Saved me a fortune!
For those in the UK, the "iFixit iOpener Kit to open Apple glued devices" from Amazon contains all the kit you need apart from the inverter cable/compressed air.