Repairs Craftsman 917.256611 Won't Start

I pulled the white wire from the relay, and on the first key turn, the fuse did not blow. However, it did blow on the second key turn. Do you think it could be the battery? I've noticed that it is not holding a charge and has to be jumped when going straight to the starter, and upon closer inspection, the battery that was on it when I bought it seems to be a bit undersized for the mower.
 
Any other ideas? I have now replaced the starter, the relay, the fuse housing, and the ignition switch. Fuse does not blow when turned to the light position, but when going to crank it does blow without the engine making a sound.
 
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