Cannot boot osx, cannot install.

Hello,

Firstly forgive me if my information is a bit basic, i'm not much of a tech savvy person!

Yesterday i was just browsing the internet and i had the spinning wheel, which rebooted my osx.

Upon return every time i entered my password, it would not boot. I tried to repair disc and verify and all seemed okay.

I read on a forum that deleting the hard drives and restoring from a backup was a good option (turns out it got me even more stuck!) I now have no option to reboot from time machine either, which i don't mind losing my data if i cannot get it back. My mac also did not come with an installation disc.

When i boot up my drive i cannot get into anything other than the installation, which fails each time and says "The os installation couldn't be completed. Gives me options of the logs and not much else.

What can i do to fix this as im at my wits end trying things but to no avail.

I can't get full details on my mac as i cannot access that but is a refurblished 2012 max and i think it was running yosemite 10.10.5, 16gb ram, 750gb hard drive (which has been partitioned.

Many thanks in advance.