Unlike other models of Raspberry Pi, if your Pi Zero doesn't detect an SD card it will show no lights at all - it will "look" dead (but 99% of the time it isn't).
Please try the following before getting in touch with support:
- Refit the SD card - With power disconnected, remove the SD card and fit it back into the Pi Zero ensuring it's pushed all the way in.
- Reinstall Raspberry Pi OS - your SD card image may be corrupt or simply too old to work with your Pi Zero. Download and write a new copy of Raspberry Pi OS to your SD card.
- Try another SD card - The card you're using may be faulty. If you have a spare SD card, try writing a fresh copy of Raspberry Pi OS to it and see if that works.
- Check your power - are you using an official Raspberry Pi power supply? If not, be careful what you try to power a Pi Zero with - many cheap USB power adapters or computer USB ports do not provide sufficient power (current).