For a Fairbanks-Morse engine, you can try this site:
http://www.hnsa.org/sound/index.htm#pampanito
Scroll down to "USS Pampanito Operating Equipment:" (about the bottom 1/4 of the page. Then look for the track titled "Main Engine Start". The track is 56 seconds long, but the actual engine in operation is from about 40 seconds to 55 seconds.