No sooner did subject present or No sooner had subject part perticiple

All three of these sentences are grammatical and have the same meaning. Astralbee is incorrect in using "came" rather than "come" - "had come" is the correct past perfect tense, which is made up of a past tense auxiliary verb + past participle main verb (which in this case is "come". Sometimes the past participle is the same as the past tense; just not in this case).

It depends on the tense of your verb. If the verb is present tense then use "did"; if it is past tense then use "had":

No sooner did he come into the classroom than the light went off.

or

No sooner had he came into the classroom than the light went off.