What can I do to upgrade an old Android 4.0.3 tablet?

I have an **Asus Transformer TF101** that is running **Android 4.0.3**. The tablet can connect websites in HTTP without issue but not in HTTPS. **Most HTTPS websites are totally unreachable.** Some websites (from large institutions) are reachable after accepting several certificat issues warnings, but display badly. The clock of the tablet was set correctly. I assume the issue has to see with how the tablet is able to deal with certificates, and also with its aging native Internet browser (which is not apparently not Chrome). **I unsuccessfully attempted upgrading the tablet firmware**, but got an error message "**Internet connection error or server busy**. Please wait and try again". I assume this issue could be caused by disabled upgrade server and/or SSL certificate issues. **Is there still a way to upgrade such a tablet**, preferably without jailbreaking it?