While the nVidia chips in this model are known to fail, when they do, the symptoms are not as you describe and generally affect both internal and external displays.

Was the replacement LCD new?  If not, and it had a lot of hours on it, it may just be that the backlight or inverter failed again.

no wrong information Dell is giving a part that was tested and working, even if is not new but it is tested by the expects.

i will suggest that if you still have the same problem after changing the lcd you will update the bios and chip set, utilities and the video drivers then try again. but if still the same problem, motherboard need replacement.

The replacement was new, and included new backlight and inverter. When I run the diagnostic test (at boot), the bars displayed on the external have the same sort of distortion and corruption that would signal GPU/memory problems on a desktop.

I'll update the bios and see what happens. Are there any other tests I can perform to try and narrow down the cause of the problems with this laptop?

Before you pay to do this, note that the D620 is among those Dell has extended the warranty for - by one year beyond the end of the warranty you purchased at the time you bought the system:

http://en.community.dell.com/blogs/direct2dell/archive/2008/08/18/nvidia-gpu-update-dell-to-offer-warranty-enhancement-to-all-affected-customers-worldwide.aspx

if the problem is happening on both lcd and external monitor it need the update and if still nothing is helping, you can replace the motherboard.

Thanks

Just for google purposes, I replaced the system board and LCD.This solved the problem; neither worked without the other, but with both parts replaced the system works just fine.