For the issue of the phone not holding your charge, it seems like your battery is of no use. You will most likely to have to get that replaced. As for the wifi greyed out, try these steps:
1.Restart your iOS device.
2.Make sure that airplane mode is off by tapping Settings > Airplane Mode.
3.Reset the network settings by tapping Settings > General > Reset > Reset Network Settings.
This will reset all network settings, including Bluetooth pairing records, Wi-Fi passwords, VPN, and APN settings.
4.Make sure that your device is using the latest software. To do so, connect your device to your computer and check for updates in iTunes.
If that doesn't work, you can always try to turn Airplane Mode and Do Not Disturb "ON" and power down the phone, turn back on, then turn those settings "OFF". For whatever reason this sometimes helps refresh the WIFI setting.
If all else fails and you still cannot figure the device's issue, you may have to take it to an Iphone store and have it repaired, if still under warranty, you can easily have the phone replaced at your nearest store.
If you have any further questions please come back and we will continue to assist in your troubleshooting needs.