***** NOT A TEACHER *****
Hello, Mr. Wai:
I do not know to whom your question is addressed, but I shall assume that anyone may answer.
1. Professor Quirk et al.'s huge book does not seem to like the terms "participle" and "gerund" very much. I do not know how they would classify that -ing word in that particular sentence. If you find out, please let us know.
2. Pence and Emery's A Grammar of Present-Day Grammar says: "The gerund ... is a hybrid. ...[I[t has the sense of a verb [my emphasis] and may take any kind of complement and any kind of adverbial modifier that a finite verb may take. ...But in addition to the sense of a verb, a gerund has the function of a noun [my emphasis] in the statement in which it appears."
3. According to Pence and Emery, "going" in "It is a question of Henry going" is a "substantive modified by the participle"; In "It is a question of Henry's going," it is a gerund modified by the substantive "in the possessive case."
4. IF you accept this claim, then, I guess that "me coming" involves a participle, and "my coming" involves, well, you can finish the sentence.
5. As has been discussed in other threads, many people say "me" in such sentences when they may actually mean "my" -- if they knew (or cared about) the rule.
6. Some people who really know their grammar (of course, that does not include me!) feel that there is a really big difference.
a. I have made up these sentences. Maybe I am the only one who sees a difference:
i. "Do you mind my asking you a question?" (That is to say, I know that you are pressed for time and that you have to leave right now, but could you spare one minute to answer a simple question?)
ii. "Do you mind me asking you a question?" (That is to say, I know that you hate me and think that I'm an idiot, but is there any chance that you will consent to answer me?)
As Pence and Emery might say, the "my" refers to the "asking" while "me" refers to the person who is doing the asking.
I think that it is accurate to say that most people who would use "me" are actually intending to convey the meaning expressed by "my" (the so-called "correct" choice).
Many books, I have noticed, simply tell learners: "me" is fine and "my" is "formal." (From reading and listening to a lot of English here in the States, I would guess that most native speakers use "me" in such cases, for it seems more "natural." That is to say, that is what they usually hear, so they assume that it is "good" English. And if most native speakers use it, then I guess that it is good English.)
Have a nice day!
James