There could be a few factors at work here:
-Your HDMI cable isn’t working (I had this with my TV which requires a specific quality of cable to work)
-Your power supply may not provide enough voltage/amperage to run the Pi. Try a different one. Note that when running, the Pi will also show a rainbow-coloured square in the top right corner of the screen if it does not have enough power to run properly.
-The software hasn’t been written properly to the SD card.