Plug in the charger and leave it charging for at least 4 hours before trying to turn it on. If the battery is totally dead, it could take a few hours to start charging. (It's called pre-charge.) And if you've regularly been using it until it turns off, you could have killed the battery, Never let it get below 40%. If it gets down to 39% and you can't charge it, turn it off. (Never charge above 80% for longest life.)
Lithium batteries are actually not the right kind of battery to use for cellphones - but they're light (lithium is the lightest metal at normal temperatures) and they can be made thin. But they can't take deep-discharge. The best battery would be a little car battery, with gelled electrolyte - a gel-cell battery. But it would weigh more than the phone and be as large as the phone. We all want thin and light (I don't, but most people do), so we get lithium batteries. And no instructions on how to care for them, because replacing batteries is a high profit business.