When you say 'brand new', do you mean brand new to you, or, just purchased 'brand new'?
What is the make/model, and, where did you get it?
Lots of saws these days are tuned a tab lean to meet some sort of EPA criteria.
A lot of guys will have the dealer re-tune the carb to perform better.
HTH

once a saw is hot you don't need to choke it, other than pushing the primer button once or twice, setting the throttle (but usually thats not necessary when the saw is hot), it should fire right off providing you got the ignition switch on and the saw is not defective.

I ususally hold the saw in one hand with the throttle wide open and push down and pull the rope. Not recommended for the beginner or a heavy saw? you have to be REAL careful where the bar and chain are. Proper way would be to set the saw on the ground, lock the chain with the chain break, set the throttle and choke if cold, flip the switch place you knee on top of the saw behind the handle/chain brake and pull like on "porkie's revenge". A new saw should fire off, if the throttle is set to half open you will have to trip if off to idle, pull back on the chain break and you are read to cut.