After searching around the 'net and find various solutions to this problem, I decided to use the concepts I had learned to put my own method to work for me. The only tool you will need for this is the Ultimate Boot CD. Download this ISO, it is very useful for other things besides being necessary for this tutorial.
* So, I first went into VirtualBox, made a new hard drive (this time with ample space + 15 GB extra). We'll call it HD2. HD1 will refer to the old bootable, but no free space, drive.
* Add the newly created disk to the list of available drives for the guest OS (in my case, Windows Server 2008).
* Boot the UBCD ISO by mounting the ISO as a CD-ROM inside of the VirtualBox settings. Sorry, the details of this are outside of the scope of this entry.
* Use the tool inside this CD (under the menu option of Hard Disk Cloning Tools) called HDClone. This will let you clone one disk to another. Do this, and find something else to occupy your time for an hour or two. The free version of this tool only clones at ~ 4 MB / second.
* When this is finished, go into VirtualBox, set the new drive as your primary boot device and boot your guest system up.
* Inside of the Guest OS (once again, this is from a Windows Server 2008 point-of-view), right click "Computer", click Manage. From here, go to storage and tell Windows to extend your primary hard drive. It will only be as big as old HD1 right now, until you extend it to a newer, more comfortable size.
And this is it. You should now be good to go, with a larger hard drive.
Wes