Q: locked startup disk

I try to reinstall OS X  from Disk Utilities on my 2007 Mac but i am told my startup disk is locked. How do i unlock it?

The Mac was not starting up, it would get halfway through the progress bar on the startup screen (grey screen) and then shut down - black screen. I reset the PRAM, reset the SMC, checked for peripheral problems - there were none, tried a safe boot - that did not work and then tried Startup Manager. In startup manager it would not boot when I chose my startup HD but it did boot when I chose the disc labeled "recovery 10.11.2". That is how I ended up in Disk Utility.

First Aid did not work on my startup HD - the reason was " file system verify or repair failed". Now I tried to reinstall OS X on the start HD and cannot do it because the drive is locked.