If this is a new installation of TurboTax, try this:
First, close TurboTax.
Right-click on your desktop TurboTax icon, and choose Properties.
In the Properties popup, go to the Compatibility tab.
Place a checkmark for "Run this program as administrator."
Click Apply and OK/Save.
Launch TurboTax, and see if it still asks you to activate.
Other users have reported that turning off anti-virus programs worked. Here's info on How to Turn Off Anti-Virus Programs. I'm assuming that you tried both pasting your activation code and manually entering it?