In most monitors the heater voltage is derived from a secondary of the high voltage system. In the case of a G05, the heater voltage is *not* derived from the HT circuit, but rather supplied by the power brick in the bottom of the cab.
So, having a dead HT circuit, or bad HT diode, should not be causing a lack of neck glow (or heater operation). Additionally, if the HT was the only issue, you should be getting deflection chatter (although it can be hard to hear).
I take it the spot killer is not lit on the deflection board? If you unplug the game board and turn the machine back on, is the spot killer lit? It should light with the game board unplugged since there is no signal coming into the monitor, if not the monitor isn't working at all.
Sounds like you may have some power related issues. Good place to start would be to grab a schematic for your cab and verify the monitor is getting proper voltages.
D