What could cause a chainsaw chain to stop moving

Both. Initially you may find that hand sharpening is kind of slow but once you get the hang of it, and realise you really only need to just slightly touch up each tooth, you can be back cutting in about the same amount of time as it takes to swap chains, or even less.

Always take a spare chain. Even if you touch up the working one rather than swap it out, there's always a possibility of damaging the chain, necessitating a replacement.

Back home it's worth looking into the cost of having the chain(s) professionally sharpened, as opposed to the time you're going to take to do a similar job. Also, you should be able to get a bunch of sharpenings for the price of even a mediocre machine sharpener. At least that's how the costing works out where I am.

Most two cycle engines are sensitive to the newer gasoline blends that can contain up to 10% ethanol. Get a small bottle of fuel additive for small engines and add a small amount of that into your gas tank. It should run a lot better after that. I had a similar problem with my leaf blower last year and this did the trick.

Star Tron is a much better brand than Stabil by the way.

If you are still having trouble and you have already checked the spark plugs, sometimes the magneto can have a buildup of rust on the surface that prevents it from generating enough current to sustain repeated firing of the spark plug as the engine turns. Take apart the pull start mechanism on the chainsaw until the magneto is exposed, and take a fine grit sandpaper to it to rub off all the rust that has formed on it by sitting all these years. To clarify the magneto is the part that is magnetic, it should grab your screwdriver.