|The best (only!) solution is to buy a Sound Card and install it in a free PCI slot.|
The on-board sound chip on the m/board is probably a cheap chip, and they can suffer from electrical interference from other m/board components. It is the electrical "noise" generated by your PC's electronics that you are hearing.
A PC is a noisy environment, and the sound chip picks up the noise generated by all the components on the m/board.
Fitting a PCI card in the PCI slot that is *furthest* away from the power supply unit (which is a major source of noise and interference!) is the only practical way - internally - to isolate the Sound Card from all that PSU-derived electrical "noise".