Weird buzzing sound in the speakers

Hello,

this is my first post here, so if I do something wrong, please point it out. I apologise if this is in the wrong place or if it breaks any rules. This, being said, on with my problem:

I have recently bought a computer and assembled all the parts with the help of a few friends. Neither of us are professionals, but we are all studying Computer Science, so we thought it would be a good way to practice. Anyway, we *had* done this before, so we didn't make any monumental mistakes. I hope.

Everything works as it should, except for the front panel audio -- we couldn't connect all the pins (to small space to get it right), so we gave up. The real problem, probably unrelated to this, follows:

My speakers (just stereo, plain, old, nothing fancy) have a weird buzzing sound when I connect them to the computer. They work fine, probably not as loud as they should. However, when I put my hand close to them, such as to change the volume, the buzzing gets louder. I can actually wave my hand towards them and hear the difference. I start noticing the buzzing get louder at probably 4 inches distance.

At first I thought it was the speakers (as I said, they are old and pretty much the chepest I could find). But when I connected them to my old computer, there was no more buzzing. This leads me to believe the problem is with the new computer, but I have no clue where to start (or even if I should attempt to fix it or take it to a professional).

I tried connecting a pair of headphones to the new computer and could hear no buzzing, but the maximum volume was way lower than the same headphones on the old computer.

Has anyone faced anythig similar? If so, what could be the cause?

Thank you in advance,
Vlad