Hard drive failure is easy to identify, in most cases the system will not boot and the BIOS will not detect it.
First item to check here is that the hard drive powers up. For most conventional hard drives, the way you tell if a hard drive powers up is simply buy touching or holding the hard drive on the label side. You will feel the rotating disks and vibration when the hard drive is powered up. Open the PC case and connect a different power plug to the drive so we can establish power in the plug and good connection.
Second item to check is that the SATA interface cable is connected and seated properly at both ends. Borrow your optical drive cable just to see if you can get it to recognize on with the BIOS.
Third item to check is the BIOS itself. Rule out that no one has altered your BIOS settings. If you are unsure about the values, reset all the settings to default settings or optimal settings
If the hard drive is recognized by the BIOS but the disk makes some clicking noise as it spins then it is also an indication that you have got a hard drive failure.
Lastly , there are few but common cases where none of the above is conclusive but the disk is failing. For these cases you will need to run some software based testing.
A lot of new computer models nowadays come with built in BIOS based memory test and hard drive test utilities, take advantage of those tools and run the tests. If your PC model did not come with such a tool, you can always download a freely available Drive Fitness Test ISO to burn onto CD. This CD will allow you to boot-up with it to run the hard drive test utility.