Unidentified clicking sound from the uni-body of Macbook Pro and the Mac takes forever to shut down

Run an Apple Hardware Test and see if any anomalies are developed.

Open Disk Utility and see what the S. M. A. R. T. is.

Make certain you have your data backed up.

Ciao.

In addition to OGLETHORPE's advice, you might try an Apple genius bar if you can...there have been threads in the past few months about a clicking sound that turned out to be something interfering with a fan. And failing hard drives/stepping motor, make a clicking sound.

To echo OGLETHORPE, back up your data...if it is the hard drive you need to back up in the near term before you loose material.

A good explanation of Disk Utility and some things you can do is in this knowledge base artile. The links at the end of the article take you to further details. Disk Utility can tell you the state of the file system on the disk but not a great detail about the physical condition of the disk and its drive system.

I would repair permissions, though some on here do not feel there is much value in that, get an external hard drive and backup the internal drive. There are a lot of good hard drives on the market and at reasonable prices now. A source I have used is the Mac specialist OWC, http://www.macsales.com since they stand behind their products.

In backing up, use something like Carbon Copy Cloner or SuperDuper to make a bootable clone of the internal drive. That way if the drive fails you can still boot and operate your computer.

It sounds like your hard drive is dead. How old is it? They tend to die at 2.5 years.

You can take it to a different authorized support provider. Until then, keep good backups because I predict you will need them.