As long as you are still using Mavericks, there is some hope.
There should be a (hidden) Recovery HD partition on your internal drive. You can see if it's there by launching Disk Utility, and after it loads, the next to the last Menu heading (between Window and Help) is entitled Debug. Click on that, and near the bottom, you'll see the choice entitled "Show every partition...". Click on that, and you can tell right away whether the Recovery HD partition is there or not by looking at the list of "devices" in the left side. (I suspect you only have one). If it is not there, let us know, and we can tell you how to get it there.
Assuming it's there, start up your machine by holding down the Command and R keys. It will take some time to lead, but once it is, you'll see a screen with (I believe) 4 menu choices (I use TechTool Pro to do disk maintenance/repairs). One of those choices should say Disk Utility. Click on that, and you will be running Disk Utility on an "isolated environment".
You need to have Disk Utility do a Verify and Repair disk at the
Volume (ie, top) level, and then do a 1) Verify and Repair Permissions, and 2) Verify and Repair Disk at the
partition level. The
partition level should be where the OS, your applications, data files, etc. are stored. For example, the volume name on my Mac Mini is "256.06 GB Samsung SSD 840 PRO Series Media", and "below" that is my primary partition called "Macintosh SSD HD", which contains the OS, applications, etc. (I also have 3 other "partitions" at that level. They are "EFI (hidden)", "Recovery HD (hidden)", and "eDrive (hidden, and made by TechTool Pro)". Even though they are normally hidden, I can see them in Disk Utility.
So, if it was my machine I was repairing, I would first do a Verify and Repair Disk for the
volume "256.06 GB Samsung SSD 840 PRO Series Media", then do a 1) Verify and Repair Permissions, and 2) Verify and Repair Disk for the
partition "Macintosh SSD HD".
Now, it's important to realize that doing the Verify and Repair Permissions in Disk Utility only does that for
Apple software. So, after you do the steps above, and assuming you can re-start your machine, you should download the excellent freeware program
Onyx. It also can Verify and Repair Permissions, but it does it for
all software, not just stufffrom Apple. To repeat, you can get it from here:
http://www.macupdate.com/app/mac/11582/onyx
You want version 2.8.8, which is listed under "Related Links".
There are more subsequent things you will need to do to get your machine up and running "completely and cleanly", but all of that should get you almost back to "normal".
If Disk Utility cannot help you, then either your hard drive is bad, or you need a more robust disk maintenance/repair program like Disk Warrior or TechTool Pro. (There is the possibility that you can use Disk Utility to completely erase and re-format your drive, and then install Mavericks. But, you will lose all your applications, data files, etc.). And, for future reference, you need to start making a bootable backup of your system, so that you can recover easily from a disaster. In fact, that is the first thing you should have done before you upgraded to Yosemite. For that, you will need an external hard drive, and the excellent backup/cloning program entitled SuperDuper!. You can use the free version of it, although it will run somewhat slower than the paid version (only costs $27.95 US).
