I have a Dell Inspiron 8500. A couple of days ago the display started flickering and then went pretty much black. If you look on a strong angle you can still see a very faint image.

I plugged in an external monitor and that works OK. From what I've read it sounds like
the problem may be either the display, the inverter or the backlight. I would like to know
if there is a simple way I can diagnose the problem and if its something an average
person can replace/repair.

Thank you.

Hi, until the other professionals here reply, I've found a useful link for you to read through. The site's a little bit confusing but it'll help you manually understand what the problems could be. And of course, it'd be great if you could post your findings here for us to help you out after.

Laptop Screen Dim, Blank Or Black - Notebook LCD Display Monitor Problem

You pretty much already diagnosed it. You tried another monitor so that proves the computer and graphics are good. And you can see a faint image, so that points to the back light.

Replacing these not something "normal" users can do and should be left up to a qualified technician.