PSE 2021 update problem

Glenn is correct.  (AFAIK, boxed DVDs will have a serial number, not a redemption code.)  You can also use this link to take you to your Adobe account products page.  You may have to sign into your account to reach the page.  You should find a download link to the program there which will also have the latest update.

You may want to uninstall the program and download a fresh installation from this link.  It will install the latest updated version of Elements without going through the update process which sometimes causes issues.

I have to downlaod everything on a 3MB DSL-- which means, on a good day, I might hit 176Kb per second download speed. 

When I know I have something big to download I start it, and go to bed.   
I have about 15 things that could all be using bandwidth atthe same time- that's why I tend to do updates very early when I I get up at 3am or before I go to bed- My echo devices / TV / computers / tablets are not using any bandwidth- it's a system that works for me. 

Sometimes a antivirus program can "get in the way"- sometimes it might necessary to turn it off during the download-- some folks will start fussing about "never turn off your anti virus software"-  It's your call-  I've never had an issue with it since the internet began.

It might be your browser- try a different one- I stick with MS Edge simply because I like it now- last year it was firefox, during the school year I use Chrome.