I would require a few more details to diagnose the problem with your laptop. Please follow the steps below and reply with results:
1. Press the power button and check if any LED indicator lights up.
2. If you see any sign of power, check if you get to hear any beeps or any lighting pattern with the system LED indicators.
3. Check if you see any blinking cursor on the Screen or the screen is completely blank and there is no video at all.
Note: your computer might not have LED indicators or Beep Code indicators. The steps I have provided are generic steps which work for most of the system models. So that I can diagnose the issue correctly, do reply with exact System Model Number of your laptop.
Please try the below mentioned simple steps and check if this fixes the problem.
1. Power off the computer.
2. Disconnect all power connections to the computer.
3. Remove all peripherals and external devices such as monitor, keyboard, mouse, etc.
4. Press and hold the power button for 10-15 seconds and then release. This will release any Flea Power or Static Electricity stored in the computer.
5. Put the connections back and check if the issue still remains.
6. If the issue is not fixed, in your reply please include the exact System Model Number of your Acer Aspire One Laptop (such as series or model).