Trunks would still want to destroy #17 and #18 for good measure and Bulma would tell them whereabouts Gero's lab was. If they find it, they destroy the Artificial Humans. Cell would still appear due to not being aware of their deaths and without being able to surprise Trunks and get another Time Machine, his only option would be to keep draining humans to get stronger. Eventually, he'd have taken out too much of the population to remain hidden and despite being far stronger than in canon, I doubt it'd be enough for him to take on post-Rosat Vegeta/Trunks. Goku and Gohan still enter the Rosat due to Goku not wanting to be surpassed by Vegeta, Dende becomes Earth's Kami, the DBs revive Cell's victims and things are at peace.
By the time of the Boo Arc, Goku wouldn't be as strong as in canon, but still about as strong as pre-Majin Vegeta, with Vegeta still being that strong, if not stronger, due to not having a slight hiatus from training over his depression at Galu's death. Without seeing Gohan at the Cell Games though, I don't think they would've gained SS2, or would've done so very recently. Things progress the same as in canon up until the fight with Dabura, with Vegeta not turning Majin due to being content with his own power. Dabura and Babidi are killed, Boo isn't revived and things are at peace unless bringing Super into account. If so, things still progress more or less the same after the God ritual.
If they don't locate the lab, however, Cell absorbs the sleeping twins and becomes Perfect Cell very early on, though wouldn't have absorbed enough humans to have his canon power. Assuming he decides to kill all the Z-Senshi immediately, the story ends here for the main cast. If he decides to host the Cell Games to give them a chance, things go the same as in canon other than Kuririn never marrying #18, nor #17 being revived.