I agree with you for the most part, and the only reason I'm commenting is that I recently bought this keyboard for my server: http://www.amazon.com/AmazonBasics-KU-0833-Wired-Keyboard-Black/dp/B005EOWBHC, and the Amazon logo stares right at me whenever I use it.
I bought it because it was cheap and I'll barely ever need to use it, but it turned out to be quite decent.
Just to clarify, you're Master tier and you're having trouble pushing past that into Challenger? That seems pretty reasonable, to be honest. You're trying to break from top 600ish to top 200. That's not easy regardless of equipment.
I looked up the specs for your laptop, and honestly, the only thing that seems like it would make a difference is the monitor, especially just the size. There may be a slight advantage to consistently 60+ framerate, but you're already getting pretty close to that. I imagine you'd find some benefits to a larger monitor though, not as much as in an FPS, but some. That can be as easy as hooking up a second monitor. If your keyboard is having issues with wear, you can buy a reasonably priced usb keyboard that will work for you. Honestly I've been really pleased with the [amazon basics keyboard](https://www.amazon.com/AmazonBasics-KU-0833-Wired-Keyboard/dp/B005EOWBHC/ref=sr_1_4?ie=UTF8&qid=1527960238&sr=8-4&keywords=amazon+basics+keyboard), which is about $12. The only downside is it can be really loud.
If you can afford, and want, a new rig though go for it. Especially in non-league games it can make the experience a lot more enjoyable in GPU intensive environments.