Hi,
You might be able to get VNC console through virsh, if you have configured sasl auth with libvirt.
Then you could try to start the engine VM paused:
hosted-engine --vm-start-paused
then add a VNC password:
hosted-engine --add-console-password
Then try to connect with vnc and you may resume the VM:
virsh -c qemu://hostname.local/system resume HostedEngine
where hostname.local is the hostname part of the connection URI.
You might also get some insight from host logs (vdsm.log).
In my case, 99% of the cases was a storage issue that was causing engine to not be able to boot.