Before changing the battery, try tapping the starter with a heavy object, no metallic works as you might arc and spark if the area is tight. I used to hit from the bottom. If it starts, your starter is worn.
Try disassembling the top part of the motor, then heavily spray the vertical shaft with WD40 or something equal, to dislodge any minute debris that may be on the shaft that turns your blades. run the engine for 5 min or so. Then after, engage the blades very slowly to try and prevent shut down. Hope this helps.
Probably not an answer but make sure the belt is at proper tension. Make sure the water pump pulley if fully engaged and turning. See if there is a difference when the ac is on, and when its not on.