****** Dell inspiron 3437 only works external monitor********

If the system boots to Windows, it's not a BIOS problem.  Check the display settings - if they look correct, but there is no display image, you either have a bad display panel or a bad GPU (i.e., mainboard).  Hold the D key through powerup -- if you do see the built in display test (cycling solid color screens), the display is bad - meaning the mainboard is the problem.  If you don't see that, the display needs to be replaced.

Thank you for your response. I am sure the display panel is good because I took the screen panel and install in another computer ( Inspiron 5421 ), it worked no problem. Two years ago, Dell an IT told me, if video chip has problem, external and internal monitor will have same problem ( bad displaying or imagine).  The motherboard seems good because I ran the computer by external monitor non-stop 3 or 4 hours( browser internet, play dvd and video game) no any function problem such as overheating, freezing or random shutdown etc.

Any body has same problem and gets resolution?

It is very possible that a GPU can be faulty internally and display a good external image (just ask anyone who had one of the faulty nVidia chips of 2006-2009 -- very often the circuit connected internally would fail earlier due to the fact that it was used more heavily than the one connected externally).

If you're certain the screen and cable are both OK, but still can't get an internal image, AND that you do get the BIST to show the color screens as described above, replace the mainboard - either the GPU is bad, or there's a fault in the circuit that feeds the video cable - or the display connector is bad.  In all three cases, the mainboard needs to be replaced to solve the problem.

Thank you for your response. I am sure the display panel is good because I took the screen panel and installed it in another computer ( Inspiron 5421 ), it worked no problem. Two years ago, Dell an IT told me, if video chip has problem, external and internal monitor will have same problem ( bad displaying or imagine).  The motherboard seems good because I ran the computer by external monitor non-stop 3 or 4 hours( browser internet, play dvd and video game) no any function problem such as overheating, freezing or random shutdown etc.

Any body has same problem and gets resolution?

If the screen shows a good built-in self test and works elsewhere, and the system works with an external monitor, and it's not a touchscreen model, replace the display cable:

www.parts-people.com/index.php

If that doesn't get the internal screen working, replace the mainboard.

If it's a touchscreen system, the display cable cannot be replaced separately from the screen assembly.