All Classic IIs, if not yet restored, need at the very least both the logic board and analog board recapping. I wouldn't do further diagnosis until you've at least completed that step first. See where that gets you, the symptoms might change or dissapear completely after a recap. Often some chips will need thorough cleaning and/or removal and resoldering - the main ones being some logic ICs next to the battery holder/CPU, the Egret chip (responsible for the startup circuit), and the DFAC (Apple sound chip) and nearby onboard RAM chips. Make sure everything is squeaky clean after your recap.