You need Dell Quickset. If you have installed Windows 7 32 Bit use these drivers:

http://philipyip.wordpress.com/unofficial-driver-sets/latitude-d-series-laptops/latitude-d820-windows-7-32-bit/

If you have installed Windows 7 64 Bit then try the drivers from the D830:

http://dellwindowsreinstallationguide.com/driver-sets/latitude-d-series-laptops/latitude-d830-windows-7-64-bit/

However it may say unsupported system.

You need Dell Quickset. If you have installed Windows 7 32 Bit use these drivers:

http://philipyip.wordpress.com/unofficial-driver-sets/latitude-d-series-laptops/latitude-d820-windows-7-32-bit/

If you have installed Windows 7 64 Bit then try the drivers from the D830:

http://dellwindowsreinstallationguide.com/driver-sets/latitude-d-series-laptops/latitude-d830-windows-7-64-bit/

However it may say unsupported system.

Thanks for the info.  I previously installed a version of Quickset for Vista 32-bit.  It seemed to install ok, and seems to be functional, but I don't see any battery related functions, other than turning some functions on or off based on whether the laptop is on battery power or adapter power.

I should clarify further.  The battery LED on the laptop does not function, and I can find no charge-level indication anywhere (the only LED that seems to function is the hard-drive LED).  The Quickset program seems to be a higher level program, not intended to control the LED's and track battery power.  Please clarify whether or not you think I should uninstall the Quickset for Vista and install the Quickset for Windows 7 you recommended.  It seems to me that the solution lies elsewhere, but I am a novice regarding Dell laptops.

Again, thanks for your help.

That version should be fine, the version I listed is likely the same one. It will allow your FN buttons and onscreen volume and brightness displays.

Battery options are available natively in Windows 7 under power options and not within Dell Quickset.These can be found here:

Start > Control panel > Hardware and Sound > Power Options

There should also be a battery icon in the notification area natively within Windows 7. If not check if the battery shows up within the Dell BIOS setup. To access the BIOS setup, power down your Dell and press F2 when powering it up as you see the Dell logo.

Thanks for the additional info.

The Windows 7 "power options" don't appear to have any options that solve my problem.

I don't seem to have the "battery icon in the notification area natively within Windows 7" which you mentioned; that is part of my fundamental problem: no battery information.

The BIOS setup indicates under "Battery Info" that the primary is "100% Charged" and for the "Module Bay" "Battery Not Installed". 

Under "Battery Health" it indicates for the primary battery:  "This battery is performing normally."

I don't see any other battery settings under SETUP that would influence the LED operation or otherwise provide for battery info within Windows 7.

The D620 manual indicates that I have five LEDs for indicating status.  One of these is for the battery, and is said to "Turns on steadily or blinks to indicate battery charge status."  As I mentioned before, only the hard-drive LED appears to be functional.  

It seems as though I am missing some basic notebook utility software, but Dell diagnostics programs don't seem to be able to help, since I am not running the original Windows XP system

Again thanks for your help.  Please continue to offer any additional ideas you may have.

My D820 which is essentially the same model as yours but with a bigger screen has the power icon nativel:

http://windows.microsoft.com/en-gb/windows/battery-meter-faq#1TC=windows-7

You can install Dell System Software for Windows 7 in the drivers list I mentioned but as mentioned the battery should be detected by Windows by default and shown in the notification area.

What BIOS revision is your D620 at version A05 gives support for Windows Vista (and 7 is essentially Vista with improvements). You should get the latest version A10.

Thank you for that latest post.  It turns out that the battery icon was indeed turned off within Windows 7, so I now have that basic indication back.  Thank you!!

However, I still don't seem to have proper LED operation.  The BIOS revision is "A08".  I could probably live without the LED's working (now that I have the battery icon working), but it would be nice to fix the LED's if it doesn't require reloading everything.

Again, thanks for any additional help you can provide.

The LED lights are hardware and nothing to do with the OS or software. Probably the only way to fix it is to buy a new battery.