Why is my hard drive making weird noises after the power got shut down?

It is definitely not safe to open the hard-drive up. By doing so, you would risk letting dust in; the smallest amount of which could do even more damage to the drive. Besides, your chances for fixing the mechanical parts are very slim.

If the drive is still under warranty, try to have it serviced.

Can you still access the data on it? If so, make a full backup immediately!

"Weird" noises from hard drives are a sign of impending failure. The noise may be from the stepper motor, its bearings, or the drive heads. In all cases, unusual or excessive noise is a sign of a problem. If you can access data on the drive, copy everything you need from it immediately. If not, you have a few choices (in order of preference):

• If the drive is under warranty, consult the manufacturer to see if said warranty covers any sort of data recovery. Usually it does not, but best to check.
• If the data is precious, consult a data recovery company. They have the proper tools and equipment (such as a clean room) in which they can remove the data platters and avoid the faulty mechanics. If the data platters are unharmed, recovery chances are good. Data recovery vendors are expensive, however, so you will need to weigh that against the cost of rebuilding the data.
• Rarely, but sometimes, I have had success with faulty drives working briefly after being cooled off. You can let the drive cool to room temperature, or put it in a plastic bag in the refrigerator for a few hours. Depending on the type of mechanical failure, this technique might just buy you a few minutes more in which to copy data.
• Rarely, but on two occasions, I have had success by orienting the drive differently from what it was in the computer. If the drive heads are the problem, and are getting "stuck" internally, you might also be able to lightly tap the drive to coax a few minutes from it. Be warned, however, that this technique has a propensity to permanently damage the drive. Do not try this unless you are 100% sure you don't want to attempt recovery by professional means.
• If the drive's circuit board is at fault (such as a bad controller) it may be that the mechanics are unharmed. If you happen to have an identical drive, you might have success in swapping the controller boards on them. A shop I worked at has done this successfully with drives that have suffered damage to the board (such as someone driving a screw into them!). While this is probably not applicable to a drive making noise, it is still a potential option.