Files Saved or Downloaded to Desktop are Saved as Hidden?

I'm on a brand new HP computer running Windows 7 and everytime I download a file from the internet or even save files from local programs to my desktop, they are saved as some sort of hidden file...or at least they behave similar to hidden files. The difference is if I open up an Explorer window and browse to my desktop, I can see them there that way, but there is no icon on my desktop for the file. I CAN see the the saved file on my desktop if I turn "view hidden files" on...but when I look at the properties of said files, they are not actually marked "hidden." I can even copy/paste that same file in my desktop and I will see the copied file show up visually on the desktop, but still not the original file unless I browse to the desktop in an Explorer window.
When right clicking the desktop, "Show desktop icons" is turned on and I can view all of my other desktop file icons, shortcuts, etc. I've searched everywhere for an answer to this and can't find anything anywhere. Thanks for any help!