Can I get the upgrade price download if I have 2013 Elements on disc but not installed?

If you had it registered at one point, shouldn't be a problem.  During the checkout process you are given a chance to check a little box that says "Check here if you own a previous version" and you typically end up getting $20 knocked off when the price is $99, like it is now.  

Give the [purchase a try:  if you don't see the box I mentioned, just wait a few weeks forthe price to drop donw to $79, sometimes it even drops to $59- but $79 is the most common sale price.    One year I got it for $59--- You won't be able to take $20 off if its on sale for $59,