I am sorry to hear you encounter such a major issue. I will be glad to assist you though I will need some actions from your side.
You say your machine meets the prerequisites to install and use Telerik Test Studio - please share further information on what your particular environment is. Please ensure you have turned off the User Account Control - here
is an article on how to disable it.
Next thing that came across is what the reason for manual activation is? Usually when the Test Studio machine is online a crash report is automatically sent to our system in case of such. Is it possible to get the machine online and then try installation again?
If internet connection is not applicable for any reason you could enable the log through the registry as well. Here is an article
(the very bottom) how to do that. Please do so and provide the recorded log to us.