I just opened the laptop(dell inspiron 5150) to dust the fan and after closing it began to function but refused to display. I tried several times making sure that the video cable is okay but it still did not come up.
It displayed very fine on an external monitor but never on the lcd.

Try to switch video from external to internal mode using Fn+F8 keys.
Press and hold down the Fn key and at the same time press on F8 (try to press a few times if it doesn’t work).

Question about backlight testing – Should a good backlight have continuity across it’s terminals if it’s good? I was assuming yes, but all the backlights that I tested (1 out of 5 was good for sure) had no continuity when tested with an ohmmeter.

I really doubt that you can test the backlight lamp with an ohmmeter but I’m not sure 100%.
I don’t test them, I replace them.

I have a dell inspiron 6000 and I accidently dropped it from my counter top. I have replaced the backlight and the inverter and still have a dark lit screen.

Have you tried reseating the video cable on the motherboard? It’s located right under the keyboard/hinge cover. Maybe the cable got disconnected from the motherboard when you dropped the laptop.

The weird part is that the dim image shrink to 60% to the left. Other 40% is just blank image. I don’t have any invertor or CCFL lamp to test on. But I guess the whole lcd is the best way.

Do this 60/40 screen happen often?

My AC adapter has a short in it. The local shop tried a universal adapter with a couple of tips but nothing worked. If I I wiggle the cord on my original adapter, I can get enough power to max the battery at 100% within the usual amount of time.

It’s possible that the power jack inside the laptop is bad and has to be replaced. It’s necessary to disassemble the laptop and take a closer look at the power socket/jack.
In a Satellite A105 the power jack is located on a harness. If the jack is bad, you simply unplug the defective harness and replace it with a new one. That’s my guess.
Take a look at the step 21 in this laptop disassembly guide. Clock on the picture to open a big one. The red arrow points to the power jack.

Could the local shop have shorted something out and caused my laptop LCD to remain black? Would that be the inverter or the backlight?

I don’t know how this question is related to your question in the first sentence. I think you missed a part of the story.
Did you take the laptop to a local shop and after that the backlight stopped working?

1. Is it possible that the laptop is not getting enough juice to power up the laptop LCD?

2. Could the local shop have shorted something out and caused my laptop LCD to remain black? Would that be the inverter or the backlight?

Ultimately, the computer works fine except the LCD screen. It works with an external monitor, and when the lid closes it hibernates so it is not a lid switch issue. The screen is dead black, no image at all so I am trying to narrow it down to power supply, inverter or backlight. It’s a 3-year old Toshiba Satellite A105.

Thanks,
-lt775