Does the pressure hold at 40psi when cranking engine, if engine starts does pressure hold?
Remove a vacuum hose, like the PCV hose from the intake, then try starting.
The IAC(idle air control) valve opens all the way when starting an engine to allow in enough air to start, it then closes to set 1,100rpm cold idle or 750rpm warm engine idle.
If the IAC Valve is not opening all the way or at all, then engine wouldn't start or stay running.
Opening a vacuum port, like the PCV hose, allows air into engine for starting.