Q: My iPhone 4 randomly turnt off and will not turn on but if I plug it into a charger the apple sign still appears?

Hi Harryharcup10,

Welcome to the Apple Support Communities!

I understand that your iPhone is not turning on as you would expect. In this situation there are a couple of different articles that I would suggest reading over. 

First, I would suggest working through the troubleshooting steps in the following attached article to help resolve the issue. 

If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support

If the issue continues, please use the information in the next attached article to continue the troubleshooting process. 

If your iOS device restarts, displays the Apple logo, or powers off while you're using it - Apple Support

Best regards,

Joe