I have a Dell Latitude CPi R laptop. This laptop fails to boot on A/C power as well as battery power. When I switch on the laptop the power light comes on and the hard drive light blinks once and after 2-3 seconds the system shuts down. The display never comes up nor does the system fan start. In case of a floppy drive inside I can hear the click sound of it trying to access the drive just before the laptop shuts down. I completely disassembled the laptop and checked all the connections thoroughly but the problem remains.
I would test the AC adapter first. I think it’s possible that the adapter is bad and the battery is discharged. Try to remove the battery, plug in the AC adapter and start the laptop without the battery installed. Then I would try to install a test memory module or at least reseat it. Does is make any difference?
If nothing helps, you can minimize the system as much as possible and try to start it with an external monitor. Normally you need only 3 components to successfully boot a laptop and see if you have some basic functionality. These components are the system board, the CPU and the memory module. Leave only these three components and connect an external monitor. Now try turn on the laptop. You should a video on the external monitor. If you still have no video and the system still shuts down, then one of the three components is bad. I would try to swap the memory first and if it doesn’t help then most likely you have a bad system board.
About 2 weeks ago I had to repair a HP laptop with similar problems. I was able bring it back to live after I reseated the video cable on the LCD screen. The cable was half way out.