I dunno if you bought something already, but if the PC powers on, makes a clicking noise form the disk and then powers down again, the problem quite likely isn't JUST the hard drive. That would simply put you on a default screen of the motherboard, where it shows things like the amount of RAM, the type of processor, the versions of things, and a warning about you needing to select a viable boot medium.
Power button sounds more reasonable than the hard disk being pooped from the description, honestly...
It's likely better economics to have someone with basic IT skills look over the machine and determine what's really broke. Worst case scenario, if the power supply and video card are newish, buying the bits and putting them together for a PC that just has to play COD4 and COD5 should be on the nice side of $500 even with current hardware prices. mainboard, cpu and ram
Can you get into the BIOS / UEFI config screen? Usually when you turn it on it flashes a message saying press (your key here) to get into UEFI or "configuration" or BIOS or "boot-up options" or similar. If you can open the configuration that way you can see if it is able to find the disk, and you can turn off the "quick boot" so it doesn't just flash past any useful warnings. If you can't even get this far, the problem is far morelikely to be mainboard or power supply and buying a new hard drive just throws good money out the window.