RE: Dell Latitude E6510 Came without Windows 7 OS Disks, How do I upgrade the HDD without them?
Yes the hard drive is dead, you are best to replace it preferably with a Solid State Drive such as a Crucial MX100.
Follow this guide to download and create a Windows 7 Reinstallation USB:
See my A Clean Install of Windows 7 for full installation instructions:
Tech Enthusiast and Author of the Unofficial Dell Windows Reinstallation Guide