My hard drive has been on the fritz recently, but I don't think it's too far gone yet. The computer still registers the drive, but Windows 7 is being stubborn and refuses to boot. I'm new to the Linux game, and I was wondering if a system like Ubuntu when run off a USB drive will be enough to recover my pertinent data - in other words, will Ubuntu running of a USB stick be able to access my hard drive so I can back everything up?
Yes you absolutely can do it..!!!
Boot a live USB(i assume you know how to make and boot a live USB)
You will see your hard-disk as an external device(like some USB)
plug in another external HDD or USB and copy all your data.
Yes, it should! Ubuntu autu-detects all present and mountable volumes at boot. Your hard drvie should show up in the file manager's sidebar. You would then only need to click on it to browse its contents.
Note that if the partition was not cleanly unmounted before, you may need to repair it using a tool like Gparted Partition Editor.