I would call it the hydro boost section. If yours is two pieces you have the master cylinder half and the booster half. The not having any fluid at the wheel cylinders would involve the master cylinder part. If you can get them bleed but the pedal just pushes hard then that is a booster issue.
The units we are talking about are different than the vacuum booster units that are all made in one piece. You need to look at what yours has. Even better take us a picture. We are just shooting in the dark on this with out seeing what you have.