Well the screen being black doesn't mean it isn't coming on, it could just be the screen.
In the case of removing the battery.... well some are easier than others. And some are a down right major pain. Yours seems to be the latter.
If lights come on, and you hear noise (fan, hard drive, etc.) then I would try plugging in an external monitor and see if you can see things on it. If so, then the display on the laptop is the problem. If you can't see anything on the external monitor, but you are sure the computer itself is running, then it may be your graphics card.
Now if the computer isn't turning on at all, then you will need to pull the battery to test it and see if the problem is the battery being dead or something else.
Side Note: If there is a "Reset" button on the device, some have one some don't, you could try that. It will be a pinhole. I don't know your specific laptop where it is/if it is. However, if you can locate it and depress it (do not use anything sharp or risk damaging it) then you can use that to "Reset" the battery. It acts like having pulled the battery and put it back.