So I started up Sibelius today and was greeted with the photo below.  For some reason Sibelius can't find the VDL sounds.  I haven't moved them at all and haven't messed with anything either.  Anyone know how I can fix this?

Have you renamed your hard drive by any chance? Sometimes that can cause a library not to be found.

Nonetheless, there are some easy things you can do to check into this and fix it. Here's some more detailed info:
https://www.tapspace.com/hesksupport/knowledgebase.php?article=72

Thanks for the link.  I followed everything in there and everything still looks good in my folder, but it's still giving me the same "missing samples" box.

NEVER MIND!  I got it.  Apparently I was running it from a moved copy, I must have accidentally moved the original when I was cleaning up my desktop.  It works now! 

In addition, where can I store this library so it's not on my desktop and I can still use it?  I have no idea how to do that.

You may store the samples anywhere you'd like. I keep mine on an external drive specifically for sound libraries. It will require you to set Kontakt to look in the new location.

What Ted said is correct. On my laptop, I keep mine in my "Applications" folder (even though VDL isn't really an application). On my other rig, I have some external drives dedicated to sample libraries and I store it there since I don't worry about being mobile.

Once you've moved it to your desired location, simply remove the library from your Kontakt list, then re-add it, navigate to the new/permanent location, and you should be good to go!