There are a few possibilities. You should have a basic tester to help determine where to start. You would want to confirm first that there is no draw on the system and that terminals are clean and secure. These have both a stator under the flywheel which you can test for AC output out of the harness. There is also a voltage regulator which converts the AC to DC the battery can use. There are Kawasaki manuals on line and I think I have the JD manual for this as well. If you are looking for easy, buy a Battery Tender JR for about $25. That is if you have an electrical outlet near the tractor and leave it plugged in until you are ready to use it. That would at least extend the life of your battery. The PTO is taking current constantly when in use, but it will take a while to drain the battery down.

Good advise from above. On your model to check the oil, unscrew the dipstick (usually yellow), wipe it down and set it back into the tube- letting it rest on the top. Pull out and that is your reading. Use SAE 30 or 10W30 oil should you need to add. Fuel should be less than a month or so old, so take this opportunity to buy fresh. To start press the clutch in and hold, throttle lever all the way up to choke and turn the key. It may take a bit if it hasn't run in a while. Be gentle with cranking it over and only crank for up to 10 seconds at a time and letting it cool for a minute if is ornery on starting. It may be a good idea to drive the tractor w/o the deck running to get familiar with how it handles, stops etc. The deck is lowered to the position set in memory with the knob ahead and below the seat. To engage the deck, the PTO switch is pulled. This is the readers digest version. Kudos for ordering a manual. The local JD dealer may also have a similar / same model in for service that they could show you the ropes on as well. Sorry for your loss.

You can go to JD parts... http://jdpc.deere.com/jdpc/servlet/com.deere.u90490.partscatalog.view.servlets.HomePageServlet_Alt Fill in 185 in the model search field and check the box next to Exact Model Search then you can look at all the parts and all the diagrams for your 185

Thanks for the input. The fluid looks like ATF from a car. It's red but, like I said, it has sort of a weird milky quality to it. So, did someone replace 30weight with ATF? Or is it supposed to use 30weight? I went to Home Depot, Lowes and ACE and they had no "transmission fluid" for lawn tractors and that makes me think that oil may be the way to go. One thing is for sure, I'm not filling it until I find out exactly what goes in there. Thanks again for the input!