Why should I buy a whole new PSU when I could just replace the noisy fan in my existing one?

Virtually all the noise generated by a PC power supply originates from the cooling fan inside it, so simply replacing the fan with a quiet fan may seem an obvious way to go. However, if you are thinking about attempting this operation, please bear the following points in mind:

1. Your existing power supply will be designed to run with a specific amount of airflow in order to adequately cool the components inside and reducing the airflow may lead to overheating and damage to the power supply and/or PC.
2. All PC power supplies contain very high voltages and even with the power disconnected, the voltages stored in the capacitors can be easily enough to kill. It is not recommended to take the cover off any PC power supply for this reason unless you are absolutely confident of your own ability. Because of the grave dangers involved, all PC power supplies by law carry a warning label forbidding removal of the power supply case.
3. There will be no standard PC fan connector inside the power supply to use to connect a replacement fan, and it would probably have to be soldered directly into the PCB inside the power supply, or have a specialist power connector attached. This can be a tricky operation to say the least.

Please consider the above points very carefully before proceeding with an operation to replace the fan in your existing power supply!