Okay, could be 2 or three things, the first is least likely which is a weak starter, 2nd would be valves out of adjustment, 3rd, is this engine has the briggs and stratton 793880 camshaft, prone to wiping the Compression release out in it and causing hard starting.
i would remove the valve cover spark plug, and turn the engine over by hand, and watch the valves moving, after the intake valve closes, (someone may have to correct me on this) the exhaust valve should just bump open a little bit, not fully open, just a bump to relieve the strain on the electric starter. I can't remember on this engine if the compression is relieved through the intake or exhaust.
the old part number was upgraded and superceded to 84005207 and i believe it doesn't come with new solid lifters, so you'll have to order those seperate, IF it's the cam.