There's many things you can attempt to try if you are handy and have some common sense. Also practical knowledge about the parts that are inside a computer.
If it is not turning on at all no juice no lights no fans spin up, it is potentially the Power Supply that could be the problem, Power button could be broken or not attached, bad motherboard.
If this is a desktop computer, you can take the parts to a bare minimum state to get the screen to display or the computer to turn out. Disconnecting Hard drives, optical drives, using only one stick of ram, and just keep it to Motherboard, Power supply, CPU and one ram stick. Have all of that correctly installed, then power up the system to see if you get any different response.
Otherwise if you are not comfortable with doing that type of work yourself, then certainly taking it to a professional might be wise.
If it turns on but nothing displays LEDs light up, it could be a video card issue, monitor issue, ram/memory issue, motherboard issue.