How to rescue data from a drive that is having start up issues

My hard rive is making whining sounds and the computer is unable to boot up.

With the side cover of the case off, I can hear the hard drive rev up and then it suddenly lowers rpm, it may rev up again or it might not, it will attempt to start if I do a soft or hard boot.... but, either way, the computer is unable to fully boot up.
Is there any means I can use to extract info from the drive?

 

First - STOP USING THE DRIVE!!! If it is close to completely dying -from your description it sounds like it's almost dead- it may die while you're messing with it. If you have an extra hard drive laying around, install it and load Windows to it, then connect the dying drive as a secondary/slave drive and try to access and copy your data off of it. If you don't have an extra drive, download and create a UBCD4Win (or Ultimate Boot CD For Windows). It's a CD that when booted to, it runs like Windows but is entirely independent of your hard drive, allowing you more-or-less unrestricted access to your data. If the tower has 2 CD drives, and one is a burner, boot to the non-burning drive using the UBCD4Win and you can burn your data to CD/DVD. If you don't have 2 CD/DVD drives, then you'll need a 2nd hard drive (either internal or USB external) or a flash drive, and you'd plug 'em in before booting to the UBCD4Win. Basically, we need a 'remote' or 'separate' environment that doesn't rely on the dying drive. If needed, you could buy an external enclosure (like this one - it handles both IDE and SATA type hard drives - if you're not sure which type of drive you have, it handles both interfaces) and then build the dying HD into it, then plug it into a USB port on a functional PC.... there's several options and methods, and they depend on what resources you have on hand (a 2nd PC, a PC with two optical drive with one being a burner, etc), so pick the best one for your situation . . . if you have more questions, feel free to ask!

(the how-to-build-the-UBCD4Win info can be found at this link)