Why does my iMac shutdown halfway through loading on startup?

I get a chime then the Apple logo appears, then the progress bar gets to about halfway, then it shuts down.

Specs

• Late 2009 27" iMac Intel Core Duo 3.06ghz
• 128GB Samsung SSD installed in place of Optical Drive.
• Stock 1TB HD
• 12GB RAM, 2x4GB and 2x2GB. The 2x2GB sticks are the stock RAM.
• OSX Yosemite.

Background Info

• I haven't used the iMac in about a month as I have a Macbook Pro from work that I use primarily.
• I turned on the iMac yesterday and the Startup was VERY SLOW, like 5 minutes.
• I looked at some forums and saw that I should make my SSD my primary boot drive. I did this and restarted but the boot time was the same.
• Next I shutdown the computer and restarted the SMC. This made the boot time a little bit faster, maybe 2 minutes but it still wasn't acceptable.
• Next I reset the NVRAM 3x and this made a significant improvement. It was now at about 25 seconds.
• When I finally logged in I opened up Photoshop and Firefox and they both just bounced on the task bar for about 2 minutes. Photoshop finally opened but Mozilla did not. I looked in the Activity Monitor and I kept getting CrashReports that were taking up 75% of the system.
• I did some googling and it seemed like I needed to run First Aid on the SSD.
• I went to Disk Utility and tried Verifying the Disk and it gave me an error saying that it could not be verified and that I would need to open it up in Recovery Mode.
• I restarted the computer and held down CMD+R and nothing happened, it just stayed on the white screen. I held down the power button until it shutdown and the powered it back up holding option. It showed that I did not have a recovery partition (even though I remember having one in the past). It did show my Samsung Drive.
• I clicked on the Samsung Partition and it loaded about halfway then shutdown.
• I tried just starting the computer up normally without holding anything down and it would do the same thing.
• I decided that I didn't have anything on the computer that I desperately needed so I was just going to reinstall Yosemite.
• I downloaded Yosemite on my MBP and made a bootable USB drive for it. (This took about 4 hours).
• I went back to my iMac and plugged the USB drive in, turned on the iMac, and held down option (expecting that it would give me the option to boot from the USB Yosemite Installer) and it chimed, the apple logo came on, the loading bar got to halfway, and it shutdown.
• I tried this about 5 times and it did the same thing.
• I tried resetting the NVRAM and it just shuts down.
• I've tried Safe Mode, resetting the SMC, option, etc. Nothing works.
• I left it unplugged over night and tried starting up this morning and I get the same thing.
• Yesterday I took out the 2x4GB ram sticks and made sure the stock 2x2GB sticks were properly seated. I tried resetting the NVRAM and it still loads halfway and then shuts down.

I don't know what else to try. When I used it more often a couple of months ago it was very fast upon start up and running memory intensive programs like Reason, Autodesk Inventor, Parallels, Ableton Live, etc.

I am very comfortable taking the computer apart I just don't know what to look for.

Thanks for the help,

Kyle