Yeah, usually buzzing sounds are fans. Cpu and video card fans are easy enough to check, like AbecX suggested, just put your finger on it to stop the blades, and see if the noise stops as well ... if it does, time to replace. If the noise continues, it's most likely the p/s fan.
As for the modem connection, best suggestion, make a note of the brand / model of the modem, and call your ISP. They'll usually have initialization strings you can enter, and test out to see if that helps the connection issues. If none work, it could indicate a faulty modem, or faulty phone lines. I know personally, before finally getting broadband, I went through a long period of really shitty connections (and 28.8 is the max where I'm at, so really shitty ... is really shitty. I think I was averaging about 4800baud, and maxing about 9600baud most of the time
), and it turned out to be the phoneline. Hooked a phone up to it, and I could barely hear the dial-tone, over the crackles, and static.