id service your pattery. it costs litterally $5.00 and rules it out as the problem.
step 1: remove cables
step 2: remove heat cover
step 3: remove felt washers on terminals (if on.)
step 4: remove battery and place on a level surface (many leave it in the car)
step 5: wipe down and clean exterior of batter
step 6: remove battery tops (usually there are two of them)
step 7: clean battery tops to ensure there is no corrosion or debris on them
step 8: use distilled water to fill the battery to the proper level ($0.80 per gallon at local super market.)
step 9: put battery tops back on
step 10: use wire brush to clean battery terminals and cables ($4.00 at local parts store.)
step 11: use baking soda and water misture on battery terminals and cables to remove corrosion.
step 11: apply new felt washers ($0.99 at local parts store)
step 12: apply anti-corrosion gel onto terminals and cables ($0.99 at local parts store, or use petrolium jelly)
step 13: place battery back into vehicle
step 14: check all connection locations for corrosion, damage, or a loose fit.
step 15: inspect as much of the cables as possible for cracks, tears, breaks, and corrosion
step 16: apply battery cables to terminals and tighten.
step 17: brag to all your friends about how you serviced you battery like an OCD pro!