Do you have a bootable external drive? If not you can create one using a USB thumb drive and using a friends Mac install the OS on it using the OS installer application. Then test it out by using the startup manager (hold the option key during boot up) on your friends system to make sure its working. Don't forget to copy over the OS installer app on to your boot drive as you will likely need it to fix your system.
OK, now with the USB thumb drive plugged in in your system reboot holding the Option key like before. Is your system booting up cleanly? If so first make a backup of any thing important as the next step could loose something.
Use the Disk Utility application on your thumb drive to fix your internal drive. Fix the permissions first then the disk you'll likely need to run is a few times. Once the drive is repairs try restarting it on the internal drive did that fix it? If not You'll need to delete the partition and test the drive. You disk may need replacing.
If you do need a new drive think about getting a SSHD (hybrid drive) to gain some performance."
With Yosemite you should be able to hold [command] + [R] after powering up your Mac & before the startup tune is heard, that's the "bong'. This will startup your Mac on its Reserve drive which is installed when Yosemite was installed. This drive is invisible when not in use. It has a full copy of Yosemite installed on that partition, including Drive Utility. You can boot up on your reserve drive & effect any repairs to the main drive, such as reinstalling the OS
