Please described the context in which your issue exists. There are several possible scenarios.
1. You are trying to download purchased installation files, having problems doing that, and are asking for the best computer browser to be using for that download?
Assuming 1, the best guideline is, if the browser that you are using is suspect, you try one of the others from the choices of Firefox, Internet Explorer, or Chrome. I have used any of the three without issue in this regard.
The program needs to be connected to the Internet for activation and later for one time/first time activation for certain features. Here this becomes more
a matter of the Internet connection than which of the browsers is being used.
If you purchased the download of Premiere Elements 13 from Adobe direct, you should be eligible for a return/refund under within 30 days of purchase.
If you purchased from an authorized reseller, then you need to deal with the seller and the seller's return/refund policy.
For Adobe, click on the following link
Membership, Account, Payment
Payments, Invoices, Orders
If the link does not hold its set, then you will need to navigate to the Chat Panel using the above titles as guides.