It could be all manner of things. Check each part of the system as a whole - for example:
- is the display working correctly?
- is the power supply working correctly?
- is the USB power cable working correctly?
- is the display cable working correctly?
- do the connected USB devices show any sign of power/life?
There's lots of stuff to try on this Raspberry Pi forum article - there is a specific bit for the Pi Zero in the third post down. If you still need help after that, post a photo of your setup and Pi Zero here - this will help people to help you.
