Dalbridge squired for Jaehaerys II, and he probably wasn’t knighted because Jaehaerys II died unexpectedly. Like Ser Hugh of the Vale, Dalbridge wasn’t of a family sufficiently ennobled to merit a last name; unlike King Robert, who honored Jon Arryn’s memory by knighting his squire, Aerys II was rather keen to replace his father’s favorites and didn’t feel beholden to a young squire of no family of significance.
And, I would guess, unlike Ser Hugh who had Littlefinger’s gold to pay for a suit of armor, a horse, and the other necessary equipment of knighthood, Dalbridge didn’t have the money to become a knight.
As to how he ended up at the Wall, I don’t know. It could be that he remained in King’s Landing and was sent to the Wall for being a Targaryen loyalist by Tywin Lannister along with Aliser Thorne; it could be that without any other means of income, he turned to banditry or some other criminal pastime to keep body and soul together; it could be that he went of his own volition, because the Night’s Watch offers room, board, and clothing to anyone who joins.