X2 to the above. Try the starter fluid and see if that does anything. It's also worth checking the fuel pressure at the fuel rail to see what the fuel pressure is.
As mentioned above, it's likely not a battery / alternator / starter problem. However, you'd be smart to actually have the battery load tested (which any auto part store will do for free) and check the condition of the battery terminals.
From watching the video, it seems to me like it's a fuel related issue.
If you cycle the ignition multiple times (without actually turning it on) to let the fuel pump prime, does it then start up after 3-4 times of doing that?