My laptop won't power on and no lights at all? Please help!

I have an Acer Aspire 5336 series and it's about 7 years old. (I know I need a new one, but I'd like to finish backing up my important stuff on it.) It won't even think about powering on and no lights at all. I tried a new battery and new power cord, but nothing. Also, I tried what someone suggested and took the battery out and tried to power on with just the adapter. I tried to hold down the power button 10 seconds- 1 minute and then putting the battery back in, but still nothing.. I hope I can get my important stuff off. Do you know if I can fix it? THANKS