Jarrod, your engine is a 13 cubic inch (213cc) model of the first design generation, with vertical crankshaft, a Pulsa-Jet carburetor, plain main bearings, and a manual recoil starter. It was made on 15 May 1984. I don't see why exposure to the weather would do any more than cosmetic damage to a Pulsa-Jet carburetor, though there would be some rusting of the governor base and levers on top of it. The carburetor body is made of either zinc or plastic depending on your luck (zinc is better), both of which are very corrosion-resistant.
Here is the illustrated parts list for your engine:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6nlxAVJ1DajI.pdf

Here is the owner manual:
http://bsintek.basco.com/BriggsDocumentDisplay/msotJO-K_ny7tH217FzoPu.pdf

As you probably know, the Pulsa-Jet carburetor has a built-in fuel pump, and the associated diaphragm may or may not have deteriorated in the 27 years since it was built. However it is only a few minutes work to replace it.

When you post pictures of the engine we will learn whether it is a light duty type or an Industrial/Commercial (I/C) type.

Parts for most Briggs engines are available from the Outdoorking on-line store, as well as from various other places. Yours is not an uncommon engine and there are probably several Outdoorking members who can help you with a second-hand carburetor, but at this point I see no reason to expect that there is anything wrong with your carburetor that a simple overhaul will not cure.