If the antenna wire is connected properly from the dock connector to the motherboard you can rule out an antenna issue. The no service on the 7 series usually is a result of an audio IC repair which has had too much heat applied. The baseband IC is underneath the audio IC and is under filled, too much heat causes solder balls to bridge giving the searching no service. Flexation or a heavy drop can also damage baseband. The baseband CPU will have to be removed and reballed. It will not be a cheap fix.
This problem error is usually caused by outdated iTunes or software on the device you have it connected to or a faulty charge lead. Try updating or restoring it on a different device with an updated iTunes and IOS or OS. Also use a different charging cable.
There would be one more thing you can look at and that is the connector on the logic board. Check there is no damage to the pins; you might need a magnifying glass to check properly. Other than that it will cost you money as the next step would require a reputable repairer to check the diode readings of the connector to see if there are any open or shorted lines plus check to see if it is getting power. This is not easy as you need the connectors connected and the camera app open.
You should be able to do this as long as you get the two connectors to fit properly. A word of warning. · Install a new battery Do not attempt to use no battery or the battery you originally had. This is an old phone and you don’t want to take the risk of a faulty battery sending error data to the CPU, it could cause the phone to want to update. This scenario would probably be a deal breaker if your storage is near full.
If the phone has been bent there is a good chance of broken traces and or cracked solder balls under either of the two audio IC’s or if you are unlucky enough the CPU. If you have ruled out parts this would be the next road to go down.
I think it could be coincidence that this happened after a battery change. Your symptoms are of a Wi-Fi chip that has a short under it. This would be a costly repair. It would be more economical to upgrade your phone.
First I would suggest installing a new battery. If iTunes still gives you errors while trying to update I don’t think there is much more you can do except replace the dock connector and charging cable. If you had a faulty battery for some time it could have filled the space where error logs are stored that is why it is telling you to do a restore. It will not update when the error log section is full.