Some drives, such as the WD Green, have firmware that spins down the drive after a preset period of time. This reduces the energy consumption of the drive and is generally intended for drives used as archives/file storage, rather than the main OS or a high demand situation. When a request is sent to the drive, it "wakes up" and takes a few seconds to spin up. I had a delay issue using an external green drive that would be in a constant spin-down/spin-up cycle.
Platter drives or any type of drive with moving parts make noise when the disk is spinning. However, if the noise is louder than the typical hard drive activity sound, it may indicate a bad disk controller. This may not be something that chkdsk/scandisk can pick up. Using the S.M.A.R.T. technology built into your hard drive, you can check for physical issues on the drive. According to a tutorial here, you can check the status of the drive by issuing the following commands in command prompt:
diskdrive get status
Any errors will be reported in command prompt and will help confirm if the disk is going bad.
You may also want to isolate the source of this problem by disabling hard drive spin-down in Control Panel > Power Options > Change Plan Settings > Change Advanced Power Settings > Hard Disk > Turn Off Hard Disk After: and set the value to 0. This will make it so Windows will never turn off the disk, though drives with energy saving firmware will likely still go into the energy saving mode.
If you can open up the computer case, you may also be able to determine which drive is clicking by listening closely when loading programs. This will tell you whether or not it's your OS drive or the 500GB HDD you installed.
IMPORTANT: Whenever you suspect a hard drive error, whether it's a physical problem or a file system problem, ensure that you have at least one backup of your data. Recovering data from a corrupted filesystem is a headache, and a hard drive with physical failure could be a nightmare.