Mower starts and dies after thirty seconds unless I hold the choke half on Fuel System

Running only on partial choke means it is running lean, which means the main jet is partially blocked. Choking restricts air, which richens the mixture, which compensates. Your engine is telling you what is wrong, and after a winter with fuel in the bowl it is nearly always the same thing.

Order of operations:

1. Drain the float bowl first. There is usually a bolt underneath, and on many engines that bolt is also the main jet. Catch what comes out and look at it - varnish, water and green crust are all common.
2. Take the bowl off and clean it properly with carb cleaner, not a rag.
3. Remove the main jet and hold it up to a light. You should see a clean round hole. Anything visible in there is your problem. Clean it with carb cleaner and a single strand of copper wire pulled out of some stranded electrical cable. Never a drill bit, never a sewing needle - scratch the orifice and you have permanently changed the fuelling and you are buying a carburettor.
4. Blow out the emulsion tube and every passage you can see.
5. While the bowl is off, check the float is not stuck and has no fuel inside it.

Nine times out of ten that is the whole repair, it takes 45 minutes, and it costs a can of cleaner. If it still leans out afterwards, check the fuel cap vent - a blocked vent creates a vacuum in the tank and starves it on roughly the timescale you describe. Loosen the cap and run it as a test.

Since it sat over winter, make sure you clean the tank too, or you will just re-varnish the jet you cleaned.

Also stop leaving fuel in it over winter, or use a stabiliser. Modern pump fuel with ethanol starts going off in about a month, absorbs water, and leaves exactly the varnish you are about to scrape out. Either run the tank and the bowl dry at the end of the season or fill it with treated fuel.

Before any of that, confirm it is fuel and not air. A cracked intake gasket gives an identical symptom - lean, dies, runs on choke. Spray a small amount of carb cleaner around the intake joint while it idles; if the engine note changes, you have an air leak and you are about to clean the wrong thing.

Have a $12 carb kit with a float needle and gaskets on the bench before you start. On an eight year old machine you will tear a gasket coming apart.

A tan plug means it was running right at some point. Useful thing to know before you start replacing parts.