Try an SMC reset and a PRAM reset (hold the PRAM reset for at least three chimes).
Try holding down the Option key just after the startup chime. Do you see the Apple boot picker menu?
Try connecting an external display. Boot the laptop and give it time to get to the login screen. Try pressing Command + F1 to see if the laptop will mirror the display to the external display. If not, then try logging in by typing the first character of your user account name, then press the "Return" key. Now type your password and press the "Return" key again. See if anything shows up on the external display. Try pressing Command + F1 again to try to mirror the display. If this doesn't work, then close the lid of the display to see if clamshell mode will force the video to the external display.
If this doesn't work, then power off the laptop. Connect an USB keyboard. Power on the laptop and immediately close the display to force clamshell mode and press the Option key just after the startup chime to see if the Apple boot picker menu will show up on the external display.
If you have a 15" or 17" model, then the GPU may have failed. If you cannot see the Apple boot picker menu then there is no way to force the laptop to use the Intel GPU instead of the discrete GPU. If you can see the Apple boot picker menu, then it may be possible to force the laptop to use the Intel GPU instead.
Without actually seeing the laptop it can be hard to determine if the GPU has failed, you have a bad Display Assembly, or whether you may have faulty memory. My guess is either the built-in display is bad or you have a GPU issue.
