It could be caused by a loose connection and/or the inverter failing...
Normally, when the inverter fails, or starts to fail...you'll experience what you have described...the screen goes dark, but the image is still there.
To me...this doesn't describe or fit into a video chip problem. At such a low cost...I would try the inverter replacement. I highly doubt it's anything else. However...I could be wrong...I'm only human.
If worse comes to worse...you're only out $50 as opposed to a new video card...or worse yet...a new display.
How comfortable are you with fixing laptops?
Dell has a Service Manual on-line for your machine:
D600 Service Manual