I understand that you are having an issue with your iPhone not turning on even though it shows it's charging. I know it's important to be able to use your iPhone. I'll be happy to provide some information on this.
Please take a look at the following articles for more information on this:
If your iPhone, iPad, or iPod touch won't charge
If your iPhone, iPad, or iPod touch won‘t turn on or is frozen
Let me know how that goes and have a great day!