Accidental corrupted recovery mode partition and cannot longer boot to it

PRAM Reset

On boot, hold ⌘ cmd + ⌥ alt + P + R until the second boot chime. This can fix a variety of things including problems due to recent kernel panics.

Recovery HD

On boot, hold ⌘ cmd + R to boot into the Recovery HD. If this fails, hold ⌥ alt on boot, and select Recovery from the options available.

From here, you can open Disk Utility and select Repair Disk.

Target Disk Mode

If you wish to get information from the computer, and you have another computer and some way of connecting the two, you can boot into Target Disk Mode by holding T on boot. Files can then be taken off the drive by the other computer as if it was a normal external drive.

Internet Recovery

If you have a recent backup or Target Disk Mode worked (and your Mac is post-July 2011) you can start fresh by using Internet Recovery.

Hold ⌘ cmd + ⌥ alt + R on boot to begin. A new copy of OS X will be downloaded from the internet and installed, erasing your internal drive.

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.