SSD Partition Corrupted
Sounds like a reinstall to me.

Every time you get a power-cut or you have to force-shut the power on the computer, you should run Repair Disk in the Disk Manager afterwards, because the HFS+ filesystem really is not very robust. Leave it for too long, with too many power cuts, and you could end up with an un-repairable partition.

So I sincerely hope that you had a backup, and it looks like you get to go through the OS X install procedure.

Oh - and go out and buy a replacement battery! It will be worth it in the long run, if only for providing enough power to allow you to shut down the machine properly in case of an extended power outage.