Right now, your Project references the location on the old HDD. This can be easily handled with but a click, or two.
First thing to do is to move your full Project's folder structure to the new HDD. If you have your Scratch Disks set to: With Project, you are good to go. Make notes on how your Assets (your AV's, stills, etc.) are organized, and the folder names, in which they reside. This will come in handy in a moment.
Move the entire folder structure over, exactly like it is. Here, I would make a Copy of your .PREL (the Project XML file) to a safe location with maybe "old" in the name, just to be sure.
Open your original .PREL (Project XML file) in PrE. It will start to load, and then pause, asking where is file ______.___. At this point, you will want to navigate to the new HDD and to the location of that Asset. For all Assets in that folder and in your Project, PrE will link to them all. If you have several folders in the Project folder hierarchy, you may have to do this several times. This is where those notes will help you. Once you have located all Assets, you can do a Save for the Project (remember, you still have that Copy safely elsewhere, in case something goes awry). You will be good to go.
And do note that Premiere Elements will only function properly if it (the program itself) is installed on your C drive.
Good point. Lately, many folk have decided to try and run PrPro on other HDD's. I've only seen a few trying to do the same with PrE, but it is worth mentioning.