we need more information. xp or vista/7? do you get any errors? did you recently install any new software? any abnormal shutdowns? to test for a hardware failure, use a linux livecd to bootup your computer. If the computer works, then it's a windows problem. If you get an error saying there is no OS installed, no bootable drive or hard disk is not formatted. The drive might be corrupted. You need to do a chkdsk c: /f to fix the problem.
Try booting into "safe mode" if its a windows machine where you can load the last good configuration, or deal with some drivers that your recently installed that may be preventing it from booting. Right when you turn on your machine start tapping the F8 key, and keep tapping it until you get the menu which will allow you to do that. Like the other poster said, more info would be helpful.
Jony hit the nail on the head "run a linux live cd" puppy linux would be a good test as it's a small download,when booted choose the option of xvesa (i thinks it's that one,it's the one to the right you need to hit enter on),if puppy runs etc,it means either the OS has been corrupted or a part of the hardware to the hard drive has failed i.e,cabling,hdd controller on the mobo or power issue.(you could try attaching hdd to the spare data cable if SATA or IDE if it's the older type of hdd (hard drive) & set hdd to master with any luck it may work other than that it's a matter if the hard disk is being detected at all by the BIOS,F1 should let you see if it is Check to make sure the cabling is all in it's place properly in case it's only a nudged cable
I think scorpNZ and jony definitely know what they're talking about, however as a first step, try getting it to boot into "safe mode" first IF its a windows machine. I have solved many problems by just doing that, and undoing changes that I had previously made. Like I said just start tapping F8 as soon as you turn your machine, and keep tapping until you get the safe mode menu. If it will boot into safe mode you can usually fix it from there. If you've recently installed a new video or sound driver, or a new program its your best bet. Trying that will take 10 minutes or so and if that doesn't work I would say definitely try and boot from a linux live CD. To boot from a CD or DVD you would need to change some parameters in your bios, and thats another issue. Again more information would make it easier to diagnose. You said your computer turns on, but does not boot, so I'm assuming its "hanging" somewhere during the boot process. Since no one knows what operating system your running, if its factory (OEM), or built by you, I just assumed it was a windows computer, and most likely a buggy driver, or program. Most of the time when windows won't boot its a software issue, and rarely a hardware issue, not saying that hardware doesn't fail.
