Are you using the power source that came with the Fire Stick. Some sticks are very temperamental to the source of power. Do not use the TV's usb port. If you are using the correct power source assure that your HDMI port used by the fire stick is the same one selected by your TV as its input source. If it does not work try a different TV to assure that your Fire Stick is not defective.
If I understand properly, your television is on HDMI2 and your television is displaying no input. If your television input source is HDMI 2 and the Fire Stick is in HDMI2 port, try changing to another HDMI port and change the input source on the television. If that still does not work, try a different television. If the Stick's screen is still blank on the television your stick might be defective. Your remote is not the issue. Even before you pair your remote, if the Fire Stick is working, you will see the boot sequence associated with the stick (e.g. the Fire Stick splash screen). If you do not see the splash screen either the HDMI port is defective, the Fire Stick is defective, or you do not have the television input to be on the HDMI associated with the Fire stick.