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A picture certainly wouldn't hurt, but the serial if associated with the powerhead, is normally enough. What I mean by that is, if the powerhead is original to the bracket (where normally the info plate is contained).
With the cylinders turning on and off, I believe you are referring to the 115/125 horse 4 cylinder models that are generally referred to the 2+2's.
The carbs are different for 2 of the cylinders and the ignition only fires two of the cylinders until it reaches a certain rpm. The two (non-firing cylinders) do get a small fuel/oil charge to keep them lubricated but they don't fire (or don't fire with enough "umph" to actually contribute).
Someone else can chime in here, but I'm thinking these did not come into existence until the 1989 model year with a serial starting 0Cxxxxx. However, I work primarily on 25 horse and under models so the 2+2's may have come into the market earlier than I think.
(after looking over some of my notes I am now more confident that the 2+2 design was introduced for the 1989 model year when they changed the 4 cylinder block to loop charged from cross flow making it quite unlikely that you have a 2+2 model).
http://www.marineengine.com/parts/mercury-outboard-parts/115-6-cyl/7191308-thru-7208847-can
I am finding it as a 1982 according to maxrules model year guide but year is not important I will give a look at oldmercs.