Bad neutral? Now days, the power switch on most TVs isn't a real power switch. There is an always-on low voltage supply that powers up the remote receiver, timer (if any) and monitors the power button. If the device on the other side of the open neutral also has a similar power-on circuit, the two in series won't let enough current flow for either to turn on. The lamp, however, allows enough current for the unknown other item to power up after three seconds. At that point, there is enough power available for the TV to turn on. In any case, they better get this fixed before they toast both the TV and whatever the other thing is.
/mike
