If it has sat with gas in the tank for a long period of time, you could have deposits that are gumming things up. Another possibility is the fuel line, It could have gone soft and a simple bend in the line could turn into a kink causing the line to collapse, restricting the floor of fuel.

First thing I'd check/replace is the fuel line.

Another thing is the filter. Frequently when a saw sits the holes in the filter will get plugged with a gummy substance.