So the 'Anti-Life Equation' is embedded within Kryptonian DNA - it's how they end up with their fantastic powers. Kryptonians were a space-faring race eons ago, sharing knowledge and technology and so forth and eventually became the bearers of bio-shielded-zero-point energy. Learning of Darkseid's quest they withdrew from the universe they had initially guided and protected, implanting genetic and mental blocks and tying themselves to Krypton and a number of tesseracts they created around their system to give themselves the illusion of still being a space-faring race (and counter-act any 'restlessness' that may eventually occur).
The secret history is uncovered by the historian and scientist Jor-El, who eventually discovers a way for new-born Kryptonians to be free of their genetic bond to Krypton ('Krypton' now isn't just the planet but also incorporates the whole tesseract system - in essence, a universe in itself (a universe they consider 'old' as there are so many red giants and ancient stars)). He shares this discovery with his best friend - Zod - who, initially shocked, becomes furious at the fact that the worlds he has helped bring knowledge to don't 'exist'...
The secret history doesn't detail the specifics as to why the Kryptonians withdrew and the reference to 'Darkseid' is misconstrued as meaning their own 'dark' natures ('the evil within'), however Zod collaborates with Non and Faora and spends decades searching for the 'truth' (Kryptonians are uber-long-lived and, as in the Byrne-version, new Kryptonians are only permitted to be 'born' when one of their number has passed away).
There are times when the trio and the El-family work together to make further discoveries and one such discovery is a way to send a receive information from beyond 'Krypton'. This new knowledge isn't shared with the rest of Krypton, the argument being that it would create that undesired 'restlessness'.
One day, when deciphering a transmission, Zod comes across a reference to 'Darkseid'. He focuses his efforts on discovering more.
Meanwhile, Jor-El discovers the secret of the catalyst-effect of certain wavelengths of 'yellow' star energy. Together with Zor-El he studies this phenomenon further and seeks to find life-sustaining worlds orbiting such stars beyond 'Krypton'. In doing so they discover the true history of the universe...and of Darkseid.
Zod's discoveries take him on a different path - the transmissions have shown that Darkseid is something so ancient and primal that, basically, 'Darkseid Is'. Taking Non and Faora into his confidence he attempts to reach out to Darkseid, to get through the tantalising whispers and get the attention of this awe-inspiring being...
The Zod Crew attempt a coup, destroying dozens of outposts and worlds and, in doing so, reveal the 'truth' about 'Krypton'. No one believes them. The El-family maintain their silence - Darkseid is coming, Zod's attempts to reach him have succeeded - their goal is to find a way to save their 'universe' and they know that if there is widespread panic, that if the 'Dark God' with his 'Hunger Dogs' and 'Para-Demons' mentioned in the Book of Rao is revealed to be true...hope would be lost.
For their crimes against Krypton the Zod Crew are sentenced to the Phantom Zone.
They swear vengeance.
In light of the deaths (and the removal of the Zod Crew) permission is granted for new-Kryptonians to be born. Jor proposes a new form of treatment prior to the gestation period. The proposal is rejected. The El-family, however, agrees to do the treatment to themselves in secret - Darkseid is coming and there needs to be hope.
Kal and Kara.
Bringers of Hope.
Their existence should convince the elder generation to permit the treatment on the new.
In the weeks prior to their gestation being completed, Darkseid attacks. Invisible. Billions are lost, stars are exhausted of their energy and the 'ancient' universe shudders. Needing a decisive leader the worlds of Krypton demand the release of Zod.
The Zod Crew shows the worlds of Krypton that the tesseracts which form their universe are being destroyed and that the shockwaves from that destruction are making their way through the fabric of their realm. Zod offers one solution:
Give yourselves to Darkseid.
The Zod Crew reveal that they now have powers beyond those of mortal Kryptonians (the destructive energies released by Darkseid's minions affected the Zone and, in turn, affected the genetic make-up of the Zod Crew)...and rain destruction on their jailers.
The El-family make the break-through they needed - the ability to send physical, organic things from 'Krypton' to the universe beyond. Because of their genetic link to this realm, the elders of the El-household cannot leave...the unborn Kal and Kara, however, can.
The sacrifice is made. With fragments of the fabric of the realm of Krypton following their wake, The Bringers of Hope are sent out in to the 'true' universe.
For millenia, billions of Kryptonians are experimented on and studied. There are whispers of two lost children...and there is hope.
For the Dark God there is only frustration. What he has spent eons seeking is before him but still hidden away. The only signs of the awakening of the AEL are the Zod Crew but their awakening is a tiny fraction of what the AEL can do and the awakening is slowly altering and destroying them.
The boy has been found.
The Zod Crew is dispatched - bring the boy home.
(sorry, was bored :p )
(of course, Zod doesn't want to be a minion any more...he wants the secret of the El-family so that he can then take his rightful place as ruler of the 'one, true universe' ('cos, you know, he's a little crazy ;) )
*and, no, this doesn't take the New Gods away from their own mythos or make Kal/Kara into Darkseid's 'counterpoint' - that is, and always will be, Orion.