I have recently had a similar issue and had a no entry sign when I try boot my mac, I found it was to do with FileVault causing the issue, i discovered this and it worked for me hope it helps 🙂
Mac Boots to No Entry Sign
This will only Help if the issue is caused by FileVault.
In order to confirm FileVault is the issue boot to cmd-r, select reinstall OS X, follow through to when you select the drive to install the OS. If it says “FileVault conversion in progress.
Use the "Security and Privacy" preference pane to check conversion status.”
To Fix
Shut Unit Down
Hold “Shift” and press power once.
When Apple Logo loads appears let go of “Shift”.
This will Boot into Safe Mode.
Go to; LaunchPad
Other
Terminal
In Terminal type in “sudo fdesetup disable”
Follow instructions regarding password and once it says FileVault has been disabled.
Shut down the unit.
You can try reboot normally, however will most likely have to reboot into cmd-r and reinstall the OS.
This will have disabled FileVault.
Once the OS is reinstalled the unit should function normally and you can turn FileVault back on in: Settings, Security and Privacy, FileVault.
My guess is that this issue is caused when the unit doesn’t shutdown correctly when encrypting files for the first time after setup.
Please Note* Do this at your own risk to loss or corruption of data, data shouldn’t be affected by this but there is a possibility.