We assume you are referring to the check engine light. It needs to turn on while the ignition is on, and needs to turn off once the engine starts running. The computer system does this to indicate that the light is working. If the light does not turn on while the ignition is in the ON position, your E300 will fail the smog test.
It should not require the removal of the entire dashboard to replace (if in fact only the bulb is defective). The instrument cluster removal alone will suffice. You should also consider California's smog check repair assistance program. They may be able to help pay for the check engine light repair on your Mercedes Benz E300, if you qualify.
California Smog Check Repair Assitance Program