Babygirl, Wow, OK. Is it really oily/greasy where the starter bolts up? Starter won't get a ground if it is oily between starter and the where it bolts to engine. Have the battery cables checked. Sometimes the corrosion is inside the cable housing and can't be seen. Just make sure the cables where ever they connect at both ends are clean (especially the ground).
Now after all that said, with new battery and new starter being checked out fine. There is only the power delivery left! My guess is that one of the cables is not making good contact or corroded inside, There by not letting the full voltage to get to starter. Hope that makes sense. Good luck and please let me know what you find even if it's not this.