1) using the battery only ( without the transformer ), and
2) using the tranformer only ( without the battery )
and see if any of the above 2 situations can start up your netbook.
If still there is nothing on the screen after power button is pressed, I believe there is some problem with the motherboard.
The only way to get back the files on the harddrive is to disassemble the netbook, take out the harddrive and put it inside a 2.5" USB portable harddrive. Then get back the files on another PC/Notebook.