My WLAN on my iPhone 7 Plus won't turn on

It's very likely a hardware issue. The chip that controls Wi-Fi has failed, but it will take a major board replacement to fix the issue. Read that as expensive, unfortunately.

Take the phone in to an authorized Apple service shop to confirm. You can find a list of shops in your area using this link: Find Locations

All things considered, the money would probably be much better spent on a new phone, since the iPhone 7 Plus cannot go past iOS 15 and newer apps are now requiring iOS 17 and iOS 18.

So, are you saying that when you tap Settings > Wi-Fi.....that the slider is "grayed out" and will not move?

If you tap Settings > Bluetooth......is that slider also "grayed out"?