New battery fully charged, but is very sluggish while trying to start.

@ralpht101 if your mower is a K-Gro then it is quite a few years old ;-) I would imagine that there is a lot of corrosion on the witring. I would start with that. Clean the cables, and apply some dielectric grease, etc. You can determine if that is one of the issues, by applying the fully charged battery directly to the starter and then "hotwire" your tractor. Carefully, it will bypass all the safety switches. If that does not help, then it is time to rebuild or replace the starter. Rebuild kit will be available through your local small engine repair place or maybe even online. You will need to have the engine number etc. for that. Not a very complicated job.

It's also possible your compression release isn't working. That makes cranking too hard for the starter to handle. In that case, it will usually begin to crank vigorously, but immediately stop when the compression stroke happens. If it is slow regardless of crank position, and turns continuously but slowly, it's the starting system.