Why wontt my iPhone 13 turn on after 30 mins of charging?

Here are a few things to try externally before you dive down the rabbit hole of opening up the phone and replacing parts.

First, swap out the cable and charger. Either one could be the source of the problem, so it's important to test with different parts to verify they're working.

Next, check the port itself. If you put your phone in a pocket, purse, or pack, there's the possibility of getting dirt, dust or lint caught in the port and interfering with the charging jack. Get yourself a magnifying glass and a bright light and check down inside the port. Use a toothpick, some 90% or higher concentration isopropyl (rubbing) alcohol and a microfiber eyeglass cloth and clean it out. Look for bent or broken pins inside the connector; occasionally a bent pin can be straightened with some fine tip tweezers, but if any are broken you'll have to replace the charging port.

Finally, try an alternative charging method; specifically see if it charges using a wireless charger. If you don't have one they can be had on AliExpress for under $5 USD or you can find reasonably priced ones just for an experiment at Amazon or eBay. If it charges wirelessly then your battery is probably okay and you again may need to replace the lightning connector.

So try out these suggestions then come back and let us know what you find. At that point we may have a better idea of what's wrong with your phone or what to try next.