Okay guys, I've just installed a new battery, given that the old one turned out to bad along with with a new starter...I'm still having the same problems.
So instead of trying to describe the problem, I've decided to upload two videos.
The first video involves what's happening when I've got the key in the ignition and attempt to start the car. If you pay close enough attention to the video at the 14 second mark, you can hear a persistent humming noise (i.e. the so called ticking noise) and see the check engine light flickering intermittently.
The second video depicts what I have going on in the engine bay.