Unfortunately, I now realised that the fan's power supply is only providing 5v at 0.07 amps to the controller - this may have been enough for the old micro-controller.
There is no micro-controller in the photos, so either the fan does not have a micro-controller or there are more parts you have not shown.
Based on your description and the photos I was going to say there is no power supply in the photos but I'll change that to if there is a power supply from mains to 5V then it is the most crude and possibly dangerous power supply I have seen in a very long time. There is nothing to isolate the mains from the rest of the board. I am guessing this is either 40 years old or built to a design that is 40 or more years old. My best guess is that it uses a resistor and capacitor to drop mains voltage, which is both crude and dangerous. It certainly does not provide the stable, regulated power that a micro-controller needs. You can't just replace the power supply components on the board, even if you do it will still be dangerous and still won't be regulated.
If this were my project I'd scrap the existing controller completely and build a new one with a proper, isolated, ready made main to 5V power supply and proper, isolated switching for controlling the fan.
It worries me that you are even doing this with your limited knowledge of electronics, it is pretty clear that you have already done things that were dangerous and I don't imagine you realised the danger.
I strongly recommend you abandon this project for a few years until you have enough knowledge that you look back at this and shiver with the thought of how dangerous it was and how close you came to killing yourself. Seriously. Either that or find a friend who does understand the risks and how to mitigate them and have your friend supervise you.