Kohler starter is there a repair kit for the starter on this ys45oo sears tractor

The SV 590 is the model designation of the Kohler engine powering the lawn tractor.

https://www.google.com/search?q=kohler+model+sv590s+parts+diagram

The 'Sears 2000 Cub Cadet' part is most of your tractor model details and the Deck Belt appears to be 42".

https://www.google.com/search?q=Sears+2000+Cub+Cadet+deck+belt

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Craftsman Replacement Belt for 42 in. Deck - Lawn ... - Sears

www.sears.com/craftsman-replacement-belt...42.../p-07133153000.. Sears
Rating: 3.5 - ‎42 votes
Jun 1, 2010 - Replacement Belt for 42 in. tractor deck. ... After a wast of time at searssaying that they could not find the belt we walked out angry and .... The Craftsman 42" Ground Hydro Drive Tractor Belt replaces manufacturers #140294.

If you had it apart and know your brushes are good, you could just order the part specified, but if I was you I would get the part and the brush kit. The brush wire actually has an eye fitting that bolts to the cap. You might have a pinched wire or, the wires might be brittle and when you go to remove the brushes, could break apart.
For your parts, google the number along with Kohler and see if you cant get it cheaper from somewhere else. In my experience, Sears is only comparable if they stock it in store and you live near by.

their are a few different filters for your rider --these are for the kohler 26 hp motor stores like home depot- lowes- sears- or small engine repair shops carry filters K&N PS-1002 http://www.sears.com/ayp-genuine-ayp-part-578416804-oil-filter-kohler-cou/p-SPM8242278631?redirectType=SKIP_LEVEL http://www.knfilters.com/oil_filter/all/kohler/sv735/26hp

If it is a V twin Kohler engine, you may have a blown head gasket. It is a common issue. Great engine but has this one issue. Kohler has a head gasket kit with improved head bolts. Torque specs are included. You will need a inch pound torque wrench and common hand tools.

Valve clearances will also effect the decompression valve in the engine, if they are too wide the valve lifter will not work and the battary will not have enough energy to crack the engine.

Just like a chevy pu, two bolts in back and one in front.
To remove strap.

More that likely its dirty. They do tend to catch some oil and dirt and get gummed up. They are easily cleaned. That can bendix can also be rebuilt for about a$66 for the rebuild kit. New starter is $150 to$265 depending on the model engine.

check for voltage at starter whe turning key to start if you have 10 or more volts the starter is bad if you have around 4 volts try tapping on starter while in the start position on key may just be froze up.if you have no voltage at starter then the solenoid may be bad.

The governor will need to be replaced