If you take a bright flash light and shine it on the built in screen, do you see any picture? Sometimes inverters burn out which power the back light. The external monitor should work, I have seen some cases where they do not work on boot or until you change a setting. That said, on the keyboard, there should be a FN key and then use one of the F1-F12 keys to switch it to the external display. I looked at some pictures of keyboards for your model and it looks like F5 is the key you will need to use. FN +F5 to switch to external.
Try to remove the battery and the power cord from the laptop, plug in the power adapter only (leave the battery out) and try again.
If you still have no picture through external or the built in display then let's move on.
DISCONNECT THE POWER ADAPTER AND THE BATTERY FROM THE LAPTOP (only plug back in to try to power on, anytime you are going to remove a part from the comptuer, disconnect all power sources first).
There should be a plastic cover on the bottom of the laptop that has a few screws in it, it covers the ram and other easily accessible things.
Remove that plastic cover and then you can try to remove the ram and put it back in. If that doesn't work, try 1 stick of ram in 1 slot at a time. Move each stick to each slot. A single bad stick of ram could be the problem or a bad slot.
Try to reset the cmos by removing all power sources, battery, power adapter and then the button cell battery from the main board if you can access it.
If it still is not working, you would need to start removing all hardware that is not needed for post, DVD drive, Hard drive, Wireless card, webcam, keyboard, mouse etc, each component can cause problems, this would require a tear down of the machine.