If by 'demagnetizer' you mean the degaussing coil around the CRT, if it burns it means the thermistor controlling its current is damaged but that would not cause the PSU to shut down. If the coil really did burn, it has most likely left a carbon deposit around the CRT which could be arcing the EHT around the glass. That would cause a loud pop noise and shut it down, causing the symptoms you describe. Look around the CRT, especially around the plastic high voltage connector, it should be clean and firmly fitted to the connector in the glass.
If the plastic cap is damaged it must be replaced, if the glass is dirty it must be cleaned. Be VERY careful if you remove the cap, before pulling it off, wire a long thin screwdriver to the metal shield around the CRT then slide the screwdriver under the edge of the cap until it meets the metal connector. Leave it there for a few minutes then remove the screwdriver and pull the cap away from the glass. There are very high voltages (maybe more than 25,000V) on the CRT and you really don't want to touch them! NEVER switch the power on without the cap refitted!
Brian.