I had a similar problem before. Upon the advice of a friend I bought an external enclosure and installed the hard drive in it. Then I plugged the external enclosure via the usb port to another computer. It read my hard drive. From there I used SeaTools from Seagate to check my hdd if it is faulty. May hdd failed all test including the Short DST-Drive Self Test which is a basic test for all hdd's. I made an RMA and Seagate replaced my faulty hdd with a new one.
I don't know what brand your hdd is but other brands like Western Digital has programs also for testing a drive if it is faulty or not. The tip of gocards22 is correct. The power supply usually has 2-3 white molex connector for IDE and 2 for SATA. If all connectors are occupied you can always buy a molex connector splitter. I use 1 since my old pc doesnt have enough connectors to power a dvd-rw / dvd-rom / 2 IDE's.
If you have connected the power cable and your old hdd is detected you can test it if it is faulty or not. Depending on your brand, there is also a number of good softwares to test a hdd like HDDScan. For Seagate you can download SeaTools for Windows at the Seagate website. There is also a SeaTools for DOS that you can use to test the hdd at boot. For Western Digital they use Data Lifeguard Tools for Windows and Data Lifeguard Tools for DOS which you will use upon boot.
If your hdd is still under warranty, they will replace your hdd free of charge.
I know it is very unfortunate to have an hdd that is not detected. For one you have the files you value (mostly personal) in it and you can't get it. It's kinda depressing when it's like that.
Hope we have helped you.