As jayeff said, you should never change parts or remove parts while connected to power. You can damage your computer and shock yourself. Not only is it unsafe for the computer it is unsafe for yourself too.
If your laptop isn't turning on, try plugging it into power with the hard drive in. If you can hear the hard drive and fans spinning but nothing appears on the screen, connect to an external display using the HDMI port on the side of your computer. Make sure the computer's charger is plugged directly into the wall outlet and not an extension cord or splitter. If it still does not work, try a different power cord and blow some compressed air into the charging port to clear it of dust. If your computer has a separate circuit board inside of it for the power button or charging port, make sure it is plugged into the main board. Some laptops will not power on without RAM cards inside of them, so make sure your RAM is seated correctly and is a working module. If none of these work, there are more things we can try, but take these steps first.