Although DC nominally claims that post-Crisis SHAZAM history remains intact, post-Zero Hour SHAZAM really starts with the Power of SHAZAM graphic novel, effectively rebooting the characters' history. The revised origin ignores the 1987 origin and attempts to recapture the tone of the original Fawcett character. Technically, the graphic novel doesn't coincide exactly with Zero Hour, but it's a particularly convenient milestone, continuity-wise. The letter column of Power of SHAZAM #23 (February 1997) encapsulate's DC's current position on SHAZAM continuity nicely:
Cap's post-Crisis continuity is kind of tricky, but here's a general guide: All his appearances in JUSTICE LEAGUE are pretty much continuity. All his appearances in his own miniseries and in ACTION COMICS WEEKLY are not. Guest appearances, crowd shots, etc., all happened unless we say they didn't.
Hardly the most satisfying answer and somewhat unusual regarding the miniseries, but at least we know where we stand (until the next Crisis-style cataclysm reorders the DC universe). :-P
In the 1994 graphic novel, Billy and Mary become orphans when their parents are killed by Theo Adam after uncovering a jewelled scarab at a Sivana-sponsored excavation in Egypt. Mary is adopted and assumes the name Mary Bromfield. Billy is entrusted into the care of his uncle Ebenezer, who keeps the money left to him for Billy's upkeep and turns Billy out into the street.
Later, Billy is guided to the cave of SHAZAM by a mysterious stranger, who is eventually revealed to be the spirit of his father, Clarence Charles Batson (the same first names and initials as C.C.Beck). After bestowing his powers upon Billy, SHAZAM is killed when his cave collapses (as tradition seems to demand, ensuring that the wizard cannot play "too" active a part in Captain Marvel's adventures).
The scarab turns out to be a focus Teth-Adam's power, after it was stripped from him and now-Black Adam had his memory erased and lead a "normal" life as Theo Adam. When "Theo" discover's the scarab's secret and transforms into Black Adam, he sets out to destroy Captain Marvel, once and for all. Their fight destroyed most of Fawcett City's World Fair exhibit, ruining Sivana's financial empire in the process.
Needless to say, Captain Marvel is successful in defeating Black Adam. SHAZAM strips Adam of his powers and memory (again), this time taking his voice as well (ensuring he can no longer call upon the powers of SHAZAM), before Captain Marvel turns him in for the murder of Billy's parents.
The first year of the 1995 monthly series concentrate on introducing the "major" characters of SHAZAM continuity. The first few issues seem to revolve around Billy's family, including Mary (who, of course, becomes Mary Marvel) and Sinclair Batson (Billy's cousin). We also see the re-emergence of Captain Nazi, who cripples Freddy Freeman, prompting Billy and Mary to bestow of portion of their power on Freddy, transforming him into Captain Marvel Junior.
The first year also shows us glimpses of the wizard SHAZAM's past and his relationship with Satanus and Blaze. (Satanus and Blaze are SHAZAM's children, birthed by a demoness who seduced SHAZAM). Blaze also facilitates the return of Black Adam. After an epic battle, the Marvel family and SHAZAM, with help from Uncle Marvel, Mister Tawny, Ibis and Bullet Man, imprison Blaze in the Rock of Eternity and banish Black Adam to a distant star.
The second year of this series starts with Billy and Freddy having a falling out, with Freddy more or less moving to New York.
Shortly after, Captain Marvel heads off to Venus on a rescue mission for some stranded astronauts. When he arrives, he finds Doctor Sivana working with a race of Venusian worms to mount an invasion of Earth. To cut a long story short, Captain Marvel uses a Boom Tube to send the worms into outer space to die. One last worm survives, the advance scout, who finds he retains the psychic abilities of his perished brethren. Thus is born the evil which is Mister Mind. :-)
The rest of the second year consists of a series of short stories, including a Captain Marvel Junior/Captain Nazi rematch, Captain Marvel/Plastic Man and Captain Marvel/Batman team-ups. Fawcett City also feels the effects of Final Night, but perhaps not as much as the rest of the Earth, thanks to a protective aura cast by SHAZAM.
Interlude #1: The 1996 Power of SHAZAM annual focuses on a young woman (Cecebeck or just plain "Beck") in a human colony on an alien world. The 1996 Dead Earth annuals are all based on the premise that Earth is long gone, remaining only as a legend to the sentients (human or otherwise) that live in the post-Earth era. In this story, it seems that Billy has survived beyond the Earth and has assumed the mantle of SHAZAM (complete with flowing beard) and resides at the Rock of Eternity. Beck finds herself at the Rock of Eternity when she is the subject of a terrorist weapon which fires "magick dust" with trans-dimensional properties. Billy (now known as the "wizard") bequeaths power to Beck and she ends up confronting one of the terrorists, who is in turn imbued with power from the Three Faces of Evil.
Interlude #2: Mary Marvel and Captain Marvel Junior featured in seperate "DC plus" issues in 1996. In Supergirl Plus, Mary has a run in with a Leesburg police officer who may or may not have attempted to molest her, depending on whose perspective on events you want to believe. Mary is all for using SHAZAM's power to mete out her own form of justice, but Supergirl persuades her to let the law take it's course. In Superboy Plus, Freddy meets up with Superboy and together they pass through an alien testing ground (for want of a better term), which forces them to confront their greatest fears. In the end, Superboy's confidence in his relationship with Superman see him through safely, whereas Freddy's doubts about his relationship with Captain Marvel are proven to be a problem for him.
End of interludes.