Just a guess...but are you absolutely sure it's your drive? The "hum" you're describing sounds more like a case fan to me. This is a lot more common. Most computers are put together with cheap fans. Usually within the first year, the fans start to make noise (a grinding, sometimes pulsating hum) that often starts a few minutes after booting the computer. Eventually, the fan will just stop, and you could end up overheating your system. A simple $5 replacement fan will fix the problem. Ball bearing fans will last longer, with less noise, than the cheaper sleeve bearing fans used in many cases.
Anyway, to make sure, try unplugging the hard drive (power and IDE cables) and starting your system for a few minutes to see if the noise occurs. Your system won't boot, but it shouldn't be damaged by this. I'll bet it's the fan!!