It's a Dell Inspiron 560 desktop. Here's the quicky tech support guide.
Mohr, we make many assumptions on these cases. (For example, you describe a very specific hard drive, and then you write "NOTHING works. My computer will not respond ... PERIOD!", and this is confusing - does the Power Light come on at all? Do you know if it's Hard Drive Failure instead of Computer's Power Supply failure? In your first note, you said some diagnostics indicated "Hard Drive Failure." So, I assume the computer's fine, the hard drive is the ONLY failure. But "my computer will not respond PERIOD" is very confusing. I have to make assumptions at this point that we're not dealing with a dead or flakey power supply.)
I suspect most of us readers are now assuming you haven't made any Recovery Disks at this point, as Dell instructs when their computers are first started. Recovery CD-DVD sets contain Windows plus all the applications to restore a new hard-drive back to it's 'from factory' original settings.
Of course, all the changes you've made, additional programs you've installed and all the data you've created will only be backed up when you've burned those to CDs or DVDs.
Dell may be able to sell you Recovery Disks for this model, but you'll need to go thru Dell. If you haven't created those when you had the chance, or haven't created data-backups, well... we've ALL been thru this painful lesson before.
Back to the hard-drive... if you have another desktop computer that can accept SATA (new, modern ones) Drives, you could plug your old C: Drive into that other, certainly-running computer and see if your old hard-drive is detected by that functional computer.
That's the quick, easy way to determine "Is my hard drive dead or not?"
If it's dead, then getting data from it will be iffy and expensive. It could be the power-module, or it could be the small electronics board on the back of that drive that has fried, OR it could be a faulty disk-mechanism inside. Solving this might cost hundreds of dollars.
There is almost no way to determine this via long-distance or by writing about it.
If another computer can 'see' your hard-drive, then it data, at least, is recoverable from it. But I'd say, "Without Dell's recovery disks, you've got about no chance to re-create Windows 7 for a new installation."