The TeamCity agent works as a system service which does not have access to GUI. This means that all processes invoked by it do not have access to GUI as well.
You can check the 'Run interactive' box for the agent service in the Services snap-in. However, you will still have to login to the machine in order to make the system to draw GUI and this will not guarantee that TestExecute will have enough permissions to access this GUI without any problems.
You need to find a way to run TeamCity build agent as an interactive app, not as a service.
You can also find more information on this topic here.