My question is: I originally downloaded Adobe Premiere Elements 10 onto my Dell laptop. It is now dead. I am thinking of buying a Mac. Can I download the second install onto the Mac. I am reading that I can run this on two computers. But, can one be a PC and one be a Mac? Thanks.
You are dealing with Premiere Elements 10 Windows and thinking Premiere Elements 10 Mac for the new Mac computer.
That means to me that you will need to purchase a new serial number/license for Premiere Elements 10 Mac if you can still find it online in stock from a retailer. If you purchased Premiere Elements 10 Windows from Adobe and originally downloaded it to your Windows computer, then all you have at Adobe are installations file specifics for your Premiere Elements 10 Windows.
There should be no problem obtaining free Premiere Elements 10 Mac tryout files from various sources even now, but that is all they will be - tryout files.
I have not run into a swap or exchange from Adobe for a non current Elements product. Perhaps the Creative Cloud applications, of which Premiere Elements is not one, has this perk. In fact, the link that you were pointed to includes
If you have an older version of a product, you must order an upgrade instead of a swap. Place upgrade orders directly with Adobe Sales. (Visit your region's Adobe Store for contact information.)
To me that spells out purchase not swap. And, Adobe Store is not going to sell you 10, rather 13.