If you need a free operating system, Ubuntu is a free option so you can get at least something running and get off the ground. I use it myself as it is free and doesn't take much to run. You can install it with a CD or USB if necessary. And if you need to run Windows applications, you can use Wine to get them going. Wine is also free. These, l find, are suitable substitutes until you can get a Windows OS installed.
It's also possible to extract your product key from the OS that was on your old hard drive, but you need to be able to boot into it, first. I've never attempted it, but I do know that it's possible, however, you need to ensure that you have the proper key for the OS you're installing.
Also, if you are using Windows 8, you may be out of luck. The serial number is tied to your motherboard, and requires deactivation before you can use it on a second computer, however, because this is only a hard drive replacement, you shouldn't have this issue.