Xbox 360: Need help diagnosing it

I’m going to paste it in

I recently bought a Xbox 360 that was made in 2011. Two problems I am having, one is that when I plug in the Xbox to the Tv, it says no signal. The second problem is that when I tried to sync the Controller to the Xbox, the controller still flashes. I know it is not a Controller problem but is a Xbox problem. I bought a new controller and replaced the batteries with new ones. I watched a videos on it, but seems like they are not a solution to my problem. If anyone thinks they have any solutions to my problem, please reply.

It sounds like the Xbox isn’t actually booting for one reason or another, the light on the front is normal though right?

The light on the front looks normal. When I click on the sync button it blinks normally and acts like it connected to the controller. But the controller still blinks slowly.