If I read right it cranks but wont start mostly hot?Then you say if you jump it it starts.Seems like low voltage hot as starter draws more hot.Id almost say check the battery cables.If it was a bad ign switch Id think it would start hard all the time.That or your dropping lots of volts hot crank.Did the battery get load tested?Even if not old or new they acn be bad and start cold not hot.Rocky