Regarding the weak signal first.
It may be that the WiFi / BT antenna cable has become loose from its' connection to the systemboard.
Here is a link to the ifixit Démontage du LG G3 D855 guide. At Step.10 in the guide you can see the antenna location.
As for not turning on. Is the Settings > Wireless and Networks > Wifi ( and BT) enable setting "greyed out" or won't hold when slid to On or that it just can't find a signal etc?
If it can't find a signal see above.
If cannot turn on then try the following:
1. Try starting the phone in safe mode to check if you can enable the WiFi / BT.
If you can then a downloaded app is the cause of the problem. The trick is to find out which one is the culprit.
2. If still no good in safe mode then try a factory restore (also known as a hard reset), of the phone to see if this resolves the problem.
Be aware that a factory restore will erase all your data and downloaded apps. It will restore the phone to its' factory default condition (or last system updated condition)
Perform a backup of the phone before you try a factory restore, using the phone's backup feature.
Once the backup has been performed, restore the phone using the phone's factory restore feature.
Once the phone has been restored to its' default condition, check if the WiFi / BT can be turned on and that you can detect networks / devices etc.
If it still doesn't work then there is a hardware fault with the phone (most likely the WiFi/BT controller on the systemboard)
If it works OK, then restore the phone, from the backup you made earlier, using the phone's restore feature.
Once the phone has been restored back to "normal", check if the WiFi /BT is OK.
If it is then the restore (reset) has resolved the problem.
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