For some reason, my heatsink fan doesn't constant spin, it only spins at intervals at a time. Is this normal? If this isn't, what could i have possibly done wrong?
It could spin faster when under full load, so it doesn't overheat. It shouldn't be problem, as long as your CPU is at a good temperature. You could be using up your PSU so that it HSF doesn't have a constant spin. What is Power Supply Unit Watts, and your PC specs?
It's pretty rare that desktop fans cut out completely. What kind of computer are we talking about here? If it's custom made, I'd look into it a bit more. I've had some fans that spun at rather low RPMs, and when the computer tried to slow it down, the fan just stopped(IE, it should be spinning at 50% but the motherboard wasn't providing enough current to turn it)
The Gigabyte 965P series I know that at low load the fan doesn't spin this is because the BIOS has a fan-throttling feature on board. You can turn it off.