if the choke is open or closed it should still start but you woud need to rev it up manually till it warms (if its stuck open) or you need to open it if its closed once it warms. is the carb you bought manual choke, automatic or electric?

 

I have seen several of those Ford sixes that WILL NOT start without a choke, even when it's is warm out.

OP, all you have to do is pull the air cleaner and look at the choke to verify it's position....

But, I guess I didn't get the part that it wasn't only hard to start, but that it wont run at all but for a few seconds, depending on the situation, it may not be the choke, or just the choke...