Hi,
If there is no video display on either the external monitor or the laptop's screen then there is a problem with the GPU (Graphics Processor Unit)on the motherboard or the motherboard itself.
In your laptop I think it is an ATI Mobility FireGL V3100 w/ 64MB VRAM. GPU. I'm not sure if it is socketed into the motherboard or hardmounted. Either way the laptop will have to be opened and the GPU inspected.
Here is a link to the service manual for your laptop. Scroll down to the section titled System Board. Here is describes the necessary pre-requisites and then the procedure in removing the systemboard so that the GPU can be either replaced (hopefully) or if not then the systemboard (motherboard) needs to be replaced.
http://www.informaticanapoli.it/download/MANUALI/Dell/precision-m20_Service%20Manual_en-us.pdf