Hi Nicolas,
If your tablet screen is not responding anymore, it is usually the fault of power saving settings making your device sleep when you don't want it to.
The first (and easiest) thing to do is make sure your drivers are all up to date.
Visit [http://support.lenovo.com/us/en/products?tabName=Downloads|Lenovo's support center] and navigate to the appropriate touchscreen drivers for your device. You'll need to uninstall your old drivers, restart the tablet, and install the new drivers.
Alternatively, you can head over to [https://downloadcenter.intel.com/|Intel's Download Center] and download the driver update utility. The utility will install the latest driver and then restart your device. After, navigate to Control Panel (found below the taskbar)>Power. Disable "Intel Display Power Saving Technology".
If you are using an external device or digitizer, and the tablet works otherwise, try disabling the power saving settings for the HID. Go to Control Panel>Device Manager>Human Interface Devices>I2C HID Device>Power Management Tab. You'll be looking for the setting labeled "Allow Windows to turn off this device to save power". There are I2C HID Device entries, so make sure to disable the setting on both.
If you tried both of those, or the tablet doesn't respond to your fingers, and are still having problems, you'll have to open your device. Pry open the back cover, unplug the MB and TS wires, and firmly plug them in again.
Hope that helps.
Happy fixing!