There’s got to be a check engine light associated with this - probably a flashing one. When you turn the key to start without cranking it, will the check engine light come on with the other dash lights? Either way I would start with a code reader to scan for existing or pending trouble codes. (I don’t think that all code readers get pending codes, so you’d want whatever one is used to do that). Large chain auto parts stores will read these for free. If you come up with any write down the exact code(s) (like P1234) and post them.
Other than that its becomes throwing darts with a blindfold on. What, exactly, did this dealer do in terms of diagnosis? (e.g. fuel pressure? compression? ignition components?) And what is the state of basic maintenance items - plugs, wires, filters…?