Might be worth trying one of these http://www.amazon.co.uk/hq-CAR-NF01-Skytronic-Ground-Isolator/dp/B000NVWB9O
- a ground loop isolator. You can get 3.5mm to 3.5mm models
but probably just cheaper to get one of the phono ones and a couple of converter plugs or cables.
Which PC output are you connecting to? Do you have separate headphone and speaker outputs? Is there a line-out on the computer? Ideally you connect the computer line-out to the amp line-in and levels should be okay. The amp guitar input will amplify a lot more (and also expects a higher impedance input) so if you really have to do that turn the computer volume right down to start with.
The guitar amp will colour the output sound, so it might be good for playing guitar through this setup, but not so great for playing music from the computer. PC speakers are generally not great; I also find headphone quality is much better, playing through a hi-fi like Alan does is a good solution, but obviously requires you to have a hi-fi near the computer and switch it on/off.