iMac Boot Loop?

I am on a Mid-2011 21.5' iMac. I have no third party RAM etc. installed.

A couple of weeks ago, my iMac began to go into a reboot loop. When I tried to boot the iMac, the iMac would go to the grey screen, the apple sign would come up, then the loader, and then blackness. This would repeat from 2-20 times before the iMac would eventually boot normally. At first, this was just a nuisance, but now I can't use my computer anymore.

When I first posted about this, I was first told to attempt to restore the OS from Recovery HD. When I tried to do this, the reinstallation would begin, then about half way through, the computer powered off, and then restarted. The cycle would then continue.

Then one day, I tried to install Yosemite. When I clicked install, it started installing, and it would get about half way in, and then turn off, repeating over and over again, leaving me unable to use my computer. I was told that without a doubt, this was a hard drive issue, so (as there was a really good offer on a 2TB hard drive to replace my 500GB), I bought a new HD. I opened up my computer, removed the old HD, and installed the new one. I expected to be able to use my Time Machine to restore all my files etc. to this working HD, but unfortunately, mid-way through booting from the USB of the Mavericks install, the screen went black. This loop continues. I attempted to install Recovery HD using Internet Recovery, but it stops about mid-way through and shuts down, restarting. I tried to reset the PRAM and SMC, but neither of these did anything.

I have no idea what could be wrong with my computer, please help.