Shade tree test of power brakes:

1. With engine off, pump brakes 5-10 times to expend any stored vacuum in the booster.

2. Place foot on brake pedal with very slight, constant pressure.

3. Start the engine.

A power booster that is working will have the brake pedal drop under your slight, constant foot pressure once there's vacuum. A dead booster will leave the pedal where it is.

Note that a dead booster and one not getting any vacuum due to other failures (cracked/plugged vacuum hose, bad check valve) will manifest the same. You need to eliminate the vacuum supply issues before condemning the booster.