A bad convergence IC almost always takes a resistor or two out with it.
On my recent Toshiba 42H82 convergence IC replacement it took out a 1.8 ohm resistor.
It's body had a hairline crack on it and was open circuit. This crack was small however metal film resistors are made by depositing a thin metal film on the outside of a ceramic core. Then a flameproof coating is applied over the metal film. So even a tiny crack can tear this fragile film and render the resistor open.
The resistor heated up so much before it blew that it turned a gold color band black. Luckily the service manual set me straight on the value.
Check the convergence output resistors with a multimeter and they should be within 5% of their printed rating.
They won't be far from the convergence ICs they are located on two big heatsinks on the signal board you can't miss them. They will have STK-xxx-xxx printed on them.
Personally I never memorized the color band values for resistors so I always go here:
http://www.dannyg.com/examples/res2/resistor.htm
Just input the color bands and it tells you the resistance and tolerance.
As for the TV powering up when the connector is removed are the tubes getting filament voltage?
If you look at the glass necks for the 3 tubes they should glow orange.