The PS4 isn't compatible with some router settings. Differences from individual router settings from person to person is usually what is the cause of connection problems, which just isn't easy to test every single configuration. Yes, PS4 is configured to identify differently than PCs and the older PSs including the PS3, so you may hit an issue with the 4 where you don't with the 3. I did too.

Login to your router through the PC.

1. WPA-PSK/WPA2 > WPA-PSK

By default, many routers are set to both and WPA2 has priority by default when both are enabled. PS4 will not work with WPA2, thus causing the immediate boots (although PS3 oddly does work when set to both.

2. AES/TKIP > TKIP.

Set to TKIP only.

3. Port forward/trigger.

The PS4 should be able to connect smoothly, but if not, you can attempt to include port forwarding. Don't have the port numbers at, though, but I think you won't need it.

Enjoy.