Hi there! Our pond is in a very similar situation as yours...it's a farm pond and it's very old, and we just started managing it. See the link below for photos and my story.

As stated above, I would get out there in a johnboat asap and measure the depth with a pole in a systematic manner and record them on a printout of your lake from Google maps. The muck in our 30-year old lake is over 4 feet deep in some places, and our lake never had cattle in it. Yours may have much, much more.