Most likely your PSU is not providing enough power to sustain the system. Is the Aerocool PSU a true power PSU? If it isn't, you will be better off getting a new PSU (get those from Corsair, Tagan, Silverstone or Seasonic). A 500W true power PSU will be enough for your build.

Based on my experience, I always have my PC shutdown automatically when I was using cheap PSU. I had never once encounter such problem after using true power PSU ever since.

i5 is sufficient for gaming. No need to spend a premium for i7.

Back to PSU, if you get the brands I've recommended, they are all true power.