iPhone not starting up?

Its must have a dead battery or a faulty battery the former is the more likely if a battery icon appears only drained still in working condition.

Try a different charging cable and a different power socket. If this does not work then your phone is broken.

First try connecting your Lightning charging cable to another USB power supply. If it works then your charger is faulty.

Next, try another Lightning cable which is known to be good. They often fail in a way where the phone acknowledges it is connected to a charger, but still cannot charge the phone. If that works then you need to buy a new Lightning cable. Even with gentle handling I find that they often fail in under two years. Where I work, we routinely issue new Lightning cables on an exchange basis (so that potentially unreliable cables do not remain in use) every two years or upon demand.

If the cable makes no difference then use a non conductive pick such as a cocktail stick to winkle out all debris, usually compacted pocket lint) from the charging socket.

After all that, if the phone still fails to charge then the phone itself needs repair: often they just need a replacement Lightning socket.

Normally when my iPad does that it's because I am using a cheap charger or there's a shortage in the socket

Take the phone to a local phone repair business and ask them what the issue is