To TS, just want to mention that iPhones are by design like that. When the battery runs flat and you charge it, you will not be able to switch on immediately. It will wait until it has enough charge before you can turn it on.

I have two iPhones and both are the same. I need to charge it at least 15-20 minutes before I can switch it on. They're just designed that way. Hope u resolve ur problem soon. Good luck