Authorities used cadaver dogs and a drone to help scour a two square-mile area, but after eight hours said they had not found any new clues to the boy's disappearance.
Aramazd Andressian Jr.'s mother reported him missing on April 22 after her estranged husband failed to drop him off at a pre-arranged meeting place.
Later that day, Aramazd Andressian Sr. was found unconscious near his BMW sedan at the park. The car had been doused with gasoline, and the elder Andressian could not account for his son's whereabouts.
After being taken into custody, Aramazd Andressian Sr. was released due to a lack of evidence, authorities said.
Flanked by relatives and law-enforcement officials, the boy's mother issued a tearful plea on Wednesday.
"There are no words to describe how heartbroken I am. Although I do not know his whereabouts, I do believe that Piqui is alive, missing his family and desperately wants to come home," Ana Estevez said, referring to her son by his nickname. "I am counting the days until I see you again, and I will never stop looking for you."
About 6 a.m. Thursday, Los Angeles County Sheriff's Department investigators and South Pasadena police -- on horseback, all-terrain vehicles and on foot -- began searching for evidence in the park and its surrounding area. They said a new tip - the only credible tip they've gotten recently in the investigation - led them to search the park again, after scouring it shortly following the boy's disappearance.
At one point during the search it appeared a cadaver dog alerted on something in a drainage ditch. Authorities opened up the drain cover and searched underneath, but did not find anything. They ended the search after about eight hours.
Sheriff's Lt. Joe Mendoza said not finding any sign of the boy gives authorities hope that he may still be alive.
"Not locating him (at the park) is obviously something of a relief and it creates optimism in our investigation," Mendoza said.
The L.A. County Board of Supervisors has offered a $20,000 reward in the case.
Anyone with information about Aramazd Andressian Jr.'s whereabouts is urged to call the sheriff's Homicide Bureau at (323) 890-5500 or provide an anonymous tip to Crime Stoppers at (800)222-TIPS.