I have a blank hard drive. Is it possible for me to install Windows XP onto it with only the product key and nothing else?
To answer the question, "Is it possible to install an OS without any installation medium?" Then the answer is yes. There are a variety of methods, such as PXE booting and disk imaging. However, these require that other factors are in place.
In your case, it sounds like none of this is set up and you are missing the installation media.
No this is not possible.
Because the operating system is made up of files. Without an installation medium, the files can't be transferred over to the computer's hard drive. The product key is simply a method of activation, it makes your copy of WinXP genuine, and that's it - no more, no less.
What are my other options?
Not many (legal, safe, virus-free) options, now that WinXP is not supported. This question is something that would have applied before, but not now, unfortunately!
Some computers would have a recovery partition, but you say your hard drive is blank, so you wouldn't have that.
Without the installation CD or DVD, then no, you cannot install the operating system as you are missing something fundamentally necessary for the operating system to work, i.e. the entire operating system.
Your only option is to get a hold of the installation disks necessary for your computer. If it is a branded computer then you could phone your manufacturer and ask if they are able to supply you a copy of the install disks (though they may charge you for them).
I would not recommend bittorrent, though many would, as you cannot easily verify that the files have not been tampered with and had malware or spyware inserted into them.
If you have simply taken a hard drive out of the computer in order to upgrade it then, potentially, you can image the old drive to the new drive using Clonezilla or similar.
I don't know any method.
Simply ask yourself - how do you install XP without any media?
If you don't use an installation CD, then you must use a USB disk. If you don't use USB disk, then you may install it from your hard disk (if your hard disk contains XP files)
If you don't use any media, then where do you get the XP installation files?
Hope you've got the answer. :)