That .part extension makes me think you use either a download manager (can very well be legal) or some P2P program like limewire (most of the time illegal, especially for paid software like roxio).
I'd find out what initiated this download and cancel it in that program.
If you don't know at all, make a new Windows account, transfer the things you want from your old account and start using the new account. Then delete the old account. It seems unlikely to me the icon will reappear on your nice new empty desktop.
I have on my desktop an icon that says:
No matter how many times I send it to the recycle bin, it keeps coming back. I have even REMOVED every Roxio program that was on my computer. How do I get rid of this icon? Thanks1