Hello Jlang,
"Not ready" is not a system default label for a task status. So you will need to check, what this status equates with.
It can be a custom status, which was added to your system or one of the default statuses, which just was renamed.
So, you will need to find out, what your company defined as "not ready" on status level.
To find the statuses, you have to go to Setup -> Project Preferences -> Statuses -> Tasks or, if your are working with different statuses on group level go to Setup -> Groups -> specific Group -> Statuses -> Tasks.
By default the Start Task button is shown for tasks, that fulfil the requirements described here.
Regards
Lars