Just definite facts
A) Graphics chipset
B) Video Cable
C) Screen Inverter
D) LCD screen
LOT of reading ahead.
1) Graphics chipset:
Connect a VGA monitor to the blue VGA port, on the right side of the laptop.http://www.geeks.com/largePic_all.asp?invtid=D620-5133-OB&pic=D620-5133-OB-box.jpg
This is a general example of a VGA port (Connector), and VGA Cable,http://en.wikipedia.org/wiki/VGA_Connector
You can use a CRT type of monitor (Looks like a small TV), or a flat LCD screen monitor if it has a VGA Cable.
Turn the monitor on. If a CRT type allow it to warm up
Turn the monitor on.
By factory default settings the display should show on the external monitor.
There are at least 3 display options;
A) Internal monitor of laptop ONLY
B) Internal monitor of laptop AND external VGA monitor
C) External VGA monitor ONLY
Press, and hold down on the Fn key, and at the Same time tap once on the F5 key.
The F5 key is the Display Toggle-Over key.
Still no display on external VGA monitor?
Hold the Fn key down again, and tap once more on the F5 key.
No display, (Or solid white), on external VGA monitor, suggests problem with graphics chipset. If this is the problem post back in a Comment.
Problem is Video Cable, or inside the Display Assembly.
(screen Inverter or LCD screen)
There are no eMachines D620 service manuals, available on the internet for free that I have seen. Supposedly a few paid for versions, but I have my reservations about that.
(Probably a Generic User Guide, which you can get for free)
I also have never worked on this model yet.
But this isn't rocket science, and this isn't 'my first rodeo'.
2) Video Cable:
The Video Cable plugs into the motherboard, in an area under the Keyboard, and under the Palm Rest Cover.
A) Top View of motherboard,http://www.ebay.com/itm/eMachine-D620-Motherboard-48-4BC01-011-MBN240100-08226-1-Yukon-MB-/121076931939?pt=US_Motherboard_CPU_Combos&hash=item1c30bf5d63
Set your mouse cursor in the middle of the photo. This enables the Zoom In feature.
Looking at the rectangular metal plate, with the opening in the middle of it; come from the Top/Left corner.
See what appears to be a fairly long white strip?
That is where the Video Cable plugs into the motherboard.
Now here is the D620 with the Keyboard removed. (And Display Assembly),http://www.ebay.com/itm/eMachines-D620-Motherboard-CPU-base-assembly-/110847874891?pt=Motherboards&hash=item19cf0c574b
Here you see the white connector again.
Middle, and towards the Top; in the small rectangular opening.
The Palm Rest Cover has to be removed, to access the Keyboard Cable's motherboard connector. This connector.
The Video Cable then goes up by the left Hinge, and then up into the Display Assembly.
From there the main portion of the Video Cable, connects to the back of the LCD screen.
There is also a separate small cable, coming from the Video Cable; that connects to one side of the screen Inverter.
Example of the Video Cable,http://www.ebay.com/itm/eMachines-D620-LCD-Video-Cable-50-4BC03-021-/130862506637?pt=US_Video_Cables_Adapters&hash=item1e7803628d
The white connector you see at the bottom, with the black pull strip; is the motherboard plug connector.
The small cable extending to the Right, connects to the screen Inverter.
The large connector shown at Top, connects to the back of the LCD screen.
Just from normal repeated opening, and closing of the laptop; the Video Cable may become pulled on, and/or pinched.
This can cause a loose connection at the motherboard side, or LCD screen side.
Screen Inverter cable connection may be pulled loose also
Can also cause damage to the Video Cable. Stretched/Broken wires
The procedure is to;
A) Remove ALL power. Remove the AC adapter (Charger), and Battery.
B) PHYSICALLY check to see if the motherboard connection is tight. Try to plug in tighter.
Reinstall power. Turn laptop on see if this was the problem.
Remove all power again. This time remove the Display Bezel, and see if the Screen Inverter cable is connected tightly.
At this point it is just going to be a visual observation, and record.
Next is to check the LCD screen connection of the Video Cable, and it may loosen the Screen Inverter connection, anyway.
[The plastic frame in front of the LCD screen is the Display Bezel,http://www.ebay.com/itm/eMachines-D620-LCD-Screen-Bezel-41-4BC01-001-/300798380595?pt=UK_Computing_Other_Computing_Networking&hash=item4608fb0a33
If plugging the connections of the Video Cable in tighter, does no good; the Video Cable is then checked for continuity.
A multimeter is used, and set on OHM's. (1K)
Electricity is sent through each wire. The reading itself isn't as important, as just seeing IF there is a reading.
No reading indicates stretched/broken wire.
You can take the Video Cable, down to the nearest small computer repair shop; and have the resident tech check it out for a few bucks.
The Video Cable MUST be ruled out as the problem, before going on. Otherwise you may be buying parts needlessly.
(LCD screen? Around $70 to $100. You have seen the price of a Video Cable)
Video Cable proves to be good? Go on.
3) Screen Inverter:
The screen Inverter is located behind the Display Bezel, and mounted to the bottom of the LCD screen. (Screen Frame)
To test a screen Inverter requires a sensitive multimeter. Read fairly expensive,http://www.fonerbooks.com/test.htm
Do to this, the ease of access to replace, and the general low cost; the screen Inverter is just replaced,http://www.ebay.com/itm/LCD-Power-Inverter-Board-for-eMachines-D620-Backlight-Replacement-for-Screen-/120819595221?pt=US_Laptop_Screens_LCD_Panels&hash=item1c2168b7d5
If this doesn't repair the problem, the problem is the LCD screen.
I can guide you, and I believe step by step; if you wish to attempt repair.
Post back in a Comment.