Any faulty component can have an adverse effect on power consumption, as every component draws power.
In your case the most likely culprit is the CPU, but don't rule out the motherboard just yet. There's still the possibility that the excess heat may have damaged it.
As for the lights flickering in your room when you start a CPU-intensive application, that could be related. The extra power required from the (damaged) CPU may be pulling too much power from the PSU, which in turn could be struggling to draw that from the wall. That's only a theory mind, and there could be a hundred other reasons. If it only started to happen after the CPU overheated, then logically, that's the cause. If that's true, I'd urge you to keep an eye on your PSU.