MB 32: Without a closing - And then he continues "Ata Kadosh" ["You are holy", the beginning of the next blessing]. The same law applies if one forgot to say "Ya'aleh Veyavo" on Rosh Chodesh in Shacharis or Mincha, and remembered after he finished the blessing: he should say it there and then begin the next blessing, "Modim", as set forth below in 422:1. As long as one did not yet begin the next blessing, it is not considered as if he has completely finished the current one, with respect to all things for which he must go back if he omitted them. This is true even though he is indeed considered to have completed the current blessing with respect to those things for which he need not go back if he omitted them, such as the mention of "Havdalah" [said after Shabbos concerning the distinction between Shabbos and the six days of the week] in "Chonen HaDaas" [the fourth blessing], and "Ya'aleh Veyavo" in the evening service on Rosh Hodesh, and "Al HaNisim" on Hanukah and Purim, etc., meaning that one does not say any of these if he already completed the blessing, even though he did not yet begin the next one - for all of these, the blessing is considered to have ended immediately when he has said "L-rd" at the end of the blessing. There are authorities who disagree, and say that even for things for which one must go back, it is as though one has begun the next blessing immediately upon concluding the current one. It seems to me that practically, if one remembers [omitting rain] after he said "L-rd", then he should not end "Who revives the dead", but rather he should end "Lamdeni Chukecha" ["Teach me Your Laws", the verse from Psalms mentioned above], and it will be as though he merely recited a verse and is still in the middle of the blessing, and then he should return to "Mashiv Haruach". One should do similarly in all cases for which one must go back if he omitted them, as I have shown in the Beur Halacha, see there.
MB 33: First - He mentioned the "first" blessings because that is the subject of discussion here, but the same applies to the last three. The reason is that the first three blessings have the same subject: setting forth the praise of the Holy One, Blessed be He, before asking for one's needs, like a servant who sets forth praise before his master before he requests something from him. The last three blessings are like a servant who received his request from his master, who praises him as he departs.
MB 34: He must return to the very beginning - Only if he erred in the closing of the blessing, e.g., he ended this blessing with the subject of another blessing, or he ended [the third blessing] during the Ten Days of Repentance with "Ha-Kel HaKadosh" ["The Holy G-d", instead of "HaMelech HaKadosh", "The Holy King"] and did not remember until after a significant pause, as then it is impossible for him to correct his mistake - because going back only helps immediately after the end of the blessing. So too in any case where if it would happen in another blessing, he would need to return to the beginning of the blessing, then in the first or last three blessings he must return to the first of the three, as they are all considered as one. But if one erred in the middle of a blessing, it does not invalidate the blessing. See above in Siman 68 in MB 1, where we explained this at length.