That would leave the mainboard as the faulty part.

http://www.golaptopparts.com/Dell_laptop_motherboard-Dell_Studio_1535_1536_1537_AMD_MotherBoard_M207C.html

It does look like the mainboard.  Could it be the LCD cable?

Could be, and it's worth trying before replacing the board

Because the laptop took a fall, the first thing to suspect is the connections going through the hinges or somewhere in the lid. 

Since the unit works fiine witn a plug-in monitor, I would seriously doubt that the problem is the mother board.  It would take a lot of force to shake anything loose on the mother board, and certainly not enough to crack the board.

I have worked on the model 1536 but only to inspect for damage when a crack developed on the case lid in the hinge area.  I recall that there are contact fingers located on both hingese suggesting that the low side of the DC power to the display may go through the hinges to get to the metal frame of the  display panel.  Just a guess, but it is possible since the contact fingers do to go the common connections of the side hinge push button PCBs. (On the othere hand, the contact fngers may be part of the antenna or just  for additional shielding).  The contac fingers are suspect since a g-force or two could have compressed the fingers so that they don't make contact anymore. 

One other thing to look at is the lid switch or whatever device senses that the lid is closed..  Most laptops have some form of switch or sensor to shutt off the display (not necessarily the entire PC) when the lid is closed.   Is there a switch or a proximity device that could have failed due to the fall?  Good l;uck.  My money is on the contact fingers.

PS:  I wouldn't worry that the display was damaged.  They are pretty rugged and the fact that the diagnostics don't detect the LCD or the inverter simply measn that they aren't communicating with the system; and loss of power will do that.

PS: 

You don't need to dismantle the laptop to inspect the contacts.  Just carefully remove the display bezel and the contacts are visible right under where the bezel covers the hinges.  The bezel is snapped into place with friction-fit clasp located around the display.  Simply, and carefully, pry the bezel away from the display (not ouward from the perimeter, but away from and perpendicular to the dusplay face),.  Move inch by inch, statrting at one corner.  A nail file or jeweler's flat screw driver will do nicely.

I have same issue with DELL inspiron 1440. i have replace the LCD cable with another one of same model but i have no luck

my screen got blank and nothing comesup. on external monitor i got this error msg 2000-0413

any idea