Have you tried to login to your account on Adobe website to see if the serial number generated for your redemption code is there. If it is there, just copy it and paste it when you are installing on a new laptop/desktop and then see if it activates. With PSE13, you need to login from within the product itself to activate the product and this is a one-time only requirements so don't worry if you are on a dodgy connection because you don't need to be only 24/7 to use the product.
Good luck.