Very odd. I know Toshiba has had many lamp and lamp power supply issues.
When you say the set attempts to fire the lamp, how do you know? What I tell customers to look for (listen for, actually) is to see if they can hear a buzzing sound coming from the lamp compartment at turn on that lasts maybe 3 seconds. That's the sound of the lamp being fired. If it doesn't light, it usually tries again.
Another trick is to remove the bulb, and while looking at the ballast (the power supply for the lamp), see if you can see a tiny blue arc of electricity near where the wires for the bulb come from. There is a spark gap there, and if you see that, that usually means the ballast is OK.
Remember that this will not work if the lamp cartridge has a sensor switch that is opened if the lamp is removed, and also won't work if the lamp compartment door isn't secure. There's definitely a sensor switch to detect that.
Let me know what you think!
I understand that if you pull out the lamp cartrige, the lamp will be disconnected, that's why I would be curious if you can see that tiny blue arc of electricity. Actually, you should be able to see it with the lamp installed unless the lamp is shorted, and that's not likely. That spark has to happen somewhere, and if not the lamp itself (where it should happen), then on the spark gap on the ballast.
The way these lamps work, by the way, is that the ballast initially applies about 2000 volts to the lamp to ionize the gas inside, then reduces the voltage to about 80 volts, and the lamps conducts electricity. So it's the initial 2000 volt and its blue arc we are looking for.
All the other noises you describe are normal.
Good luck, and let me know how it goes!
Then it has to be the lamp power supply, called the ballast. It's possible that you are missing the roughly 330 volts DC that supplies power to the ballast, and if you are comfrotable taking the set apart and have a voltmeter, you should check that. It shouldn't be too difficult to do. You can also probably replace the ballast yourself, and if you want to try that, I might be able to give you some tips.
Let me know if you want to go down that route!
I would expect the ballast to be in the $200 range, and a tech to be in the $150 range. Get a tech who is either Toshiba authorized, or knows the problems with this set. As I said, this TV has a history of lamp and ballast problems, so a Toshiba tech will know all about it.