I had a similar problem. For a long time I struggled to decide between battery and starter. Then I figured out that there is some oil on top of the valve cover gasket. This did not not look normal. So I pulled out the spark plug tubes, and low and behold there was oil at the bottom of three of my spark plugs. So I had a blown valve cover gasket causing all these other problems. I replaced the valve cover gasket, spark plugs (they were never replaced before), wires, seals, distributor cap and rotor. Essentially did a full tune up. It has been fine ever since.