You did not say if the green is for the Melbourne inner suburbs transmitter or for the main Melbourne transmitters at Mt Dandenong. This is selectable on top right of the map. "Transmitters available"
You are unlikely to get reliable reception from the Melbourne inner suburbs transmitter unless the antenna is mounted on its side (the short and long elements pointing towards the ground and not parallel with the horizon) and rotated to point towards the western end of the Melbourne CBD.
As for doing it yourself, firstly are you confident climbing on the roof?
So I finally got around to getting on the roof. I pointed my antenna at the Melbourne CBD tower, using one of the antenna helper apps (Antenna Mate). I completely lost Channel 10 after doing this (I tried both auto and manual tuning), so I repointed it back at Mt Dandenong. All of the other antenna's in the street seem to be pointing at Mt Dandenong, and most seem to have the same style antenna as I do.
I took a quick snap of my antenna while I was up there:
Any tips on what the next step should be:
1. Buy a cheapo amplifier from Jaycar ($20) and hope that fixes it.
2. Buy a new antenna