The correct option is
D went off
The phrase, 'went off' when used along with the words 'fire alarm' means 'started making a noise'. As this phrase conveys a clear meaning when used in the given sentence, option D is correct.
The phrase, 'went about' means 'started doing something that one normally does in the usual way'. Eg: Even though there was violence in some parts of the city, office-goers went about their work as usual.
The phrase, 'went out', means 'stopped working'. Eg: The lights went out because there was a power was cut.
The phrase, 'went up' means 'increased'. Eg: As summer progressed, the average temperature of the city went up.
Given the meanings as above, the phrases given in options A, B and C cannot be used in the blank to form a meaningful sentence. Hence, these options are incorrect.