It seems that there is not enough power to the fan to give it the initial extra boost it needs. Fans take more to get them spinning than to keep them spinning. The chirping noise is indicative of a fan that was never initially lubricated or has lost the lubrication. You would want to be very careful, but you could certainly try a little white silicone grease on the fan shaft where it inserts into the fan case. No lube would also explain why you need to "jump start" the fan. You can usually get the white silicone grease for electronics at an electronic supply store like Radio Shack. No guarantee, but it's worth checking into.