Welcome to the forum
It sounds to me as if your backlight has gone
You can try connecting to an external screen via HDMI cable & then check that the touchscreen is working. The external screen will mirror what is on the tablet & you will still be able to touch and get a response.
But sadly, I doubt you will get this working unless you dismantle the tablet, can get the spare parts and perform a DIY fix. Paying for someone else to repair it is going to cost more than the tf101 is worth & you would probably be better off replacing it.