Issue Martian Manhunter 1 of 4
Subtitle Fever Dream
Date May 1988
Writer(s) J.M. DeMatteis
Artist(s) Mark Badger
storyline J'onn J'onzz called out telepathically to Batman (who was taking down a serial killer) for help. He woke up in the Batcave, somewhat unaware as to what was happening. He told Batman he was sorry for endangering him, and that "he" was in the cave. Batman tried to convince the Martian that no one else was there, but he took a punch to the jaw. When he woke up, Batman momentarily saw what J'onn was talking about.
J'onn fell into and out of dreams (illusions?) about Mars. He began to think it was related to the spore he recently absorbed while on a mission with the Justice League. Batman went to the Justice League (International) and reported the same idea.

Issue Martian Manhunter 2 of 4
Subtitle Burning Bright
Date June 1988
Writer(s) J.M. DeMatteis
Artist(s) Mark Badger
storyline The Justice League found J'onn in a museum. He was still battling with what he believed was only in his mind. He remembered the Martian god of light and life, H'ronmeer, and began to believe his psyche was building a manifestation of him. The JLI finally captured him in space above Rome - he'd shut his brain down. Blue Beetle's Bug headed for Rome. Once on the ground, H'ronmeer attacked. Beetle, Booster Gold, Rocket Red 7, and Batman were disabled. Mr. Miracle betrayed J'onn to the god.
H'ronmeer took him to Colorado, to the home of Dr. Saul Erdel - the scientist who'd accidentally brought him to Earth many years before, who died in his arms due to shock soon thereafter.

Issue Martian Manhunter 3 of 4
Subtitle Who am I?
Date July 1988
Writer(s) J.M. DeMatteis
Artist(s) Mark Badger
storyline H'ronmeer set the village were Erdel lived on fire - all the houses were marked with a Martian plague warning (as was Erdel). J'onn was able to put the flames out; Erdel went looking for him after he disappeared. He returned to save Dr. Erdel from a falling building.
J'onn came to grips that he'd had amnesia and his memories were flooding him. Dr. Erdel encouraged him to let them come, but at a more manageable pace. J'onn was still confused - he didn't know if fire was a true weakness, or simply a memory of the bodies being burned due to the plague which swept Mars. Erdel took him into the lab where he first appeared on Earth.
Erdel came clean: when J'onn arrived on Earth, it wasn't him who he cradled in his arms, it was another Martian. A child. Erdel realized the child had been dead for some time and buried it. J'onn's mental (and physical) state was poor, and Erdel nursed him back to health before offering to send him home. J'onn destroyed the self-taught doctor's equipment. He used the mental bond he'd created with the Martian to help him put the past behind him and to physically reshape him into something "more acceptable" to humans.
J'onn was taken to the place where his daughter was buried. He began to believe that the machine had not only ripped him from a location, but from a time. Saul told him he'd repaired the machine; J'onn (wondering if that was his real name) asked his friend to send him home.
J'onn was yanked away, into the presence of H'ronmeer.

Issue Martian Manhunter 4 of 4
Subtitle Welcome Home
Date August 1988
Writer(s) J.M. DeMatteis
Artist(s) Mark Badger
storyline As J'onn flew across Mars with H'ronmeer, the Justice League confronted Erdel. The god told J'onn he'd not been to Mars in "centuries."
Though Batman threatened him with violence, Erdel refused to bring J'onn back until / unless he called out to him. Mr. Miracle believed the man (after having a momentary mental connection with H'ronmeer.
J'onn's family told him they were bound to Mars as long as he clinged to their memories. If he would return to Earth and cherish - not forget them - they would be able to make it to heaven. J'onn called out to Erdel that it was time for him to return home - to Earth.
The Martian Manhunter embraced the Justice League as his true self for the first time.

Notes, references to time, and chronology:
Batman has known J'onn for years: "In all the years I've known J'onn -- I've never seen him like this: so out-of-control. So -- irrational." (issue 1)
"I've been on this world for ... how many years? I can't say for sure -- but long enough to be comfortable here." (J'onn, issue 1)
This takes place during Justice League International. (multiple references).
For the first time since arriving on Earth, J'onn's memories of Mars returned. He regained his "real" form and learned he had a wife and daughter.