I went the same route, bought two batteries. Then figured out it was my solenoid not letting enough juice through.
Jump it with a screw driver.
Tom is probably right. Had a Craftsman I had to start with screwdriver across the solenoid only 6 months after I bought it. Everything on that POS mower broke except the B & S engine. Bearings, Pulleys, ETC... Finally gave it away after the steering stripped out. Wish you luck. I'll NEVER buy another Craftsman mower.