I simply cannot afford to buy or build an entirely new computer at the moment and, whilst my laptop still has a pitifully poor GPU, I feel that a better CPU would make things so much better. The few games I want to run, such as Minecraft, are more CPU intensive than GPU intensive anyway. Is it true that there is simply no way to change your laptop's CPU? Just, it seems as though finances aren't going to permit me to build a new machine for a few years to come and my 4 year-old laptop, which was only budget/mid-range at the time of purchase, isn't fairing brilliantly.

IIRC, you can't. I may be wrong. Better to ask http://www.gamesas.com/topic/1435536-the-community-tech-thread-no-124/, better chance for an answer

It's impossible to change out most laptop CPUs. The only exceptions are really systems that were designed to be high end to begin with.