Unusual Loud Beep on Start Up

May be the ABS bake actuator. Common very expensive failure item.

Do you hear the accumulator pump motor constantly cycle on and off sounds like a rattle snake behind the dash?

The dash going out is a very very common issue that unit is called the Combo meter. New rebuilt one costs $100 you install it. Not the reason your beeping that's the brakes are going to fail alert.

Both off these issue discussions can be found by using the search forums tab up top and search the words I highlighted.

 

The beep indicates the braking system hydraulic pressure is low and is not coming up as fast as it should while the pump runs. Could mean pump worn, valves not seating correctly, faulty relays or connectors powering the pump, etc.

Your Gen 2 has the most brake-by-wire-y braking system that was ever sold on a Prius. Your foot on the pedal is strictly an input, and the computer and actuator do the braking. A disadvantage of that system is your foot will likely not feel anything very much different if you are braking normally/moderately, even during a warning that the pressure is somewhat low. But if you need to brake hard and the pressure is low, it won't happen.

Gen 1 had a system with a boost chamber behind the master cylinder piston and Gen 3 brought it back, so in all the generations other than Gen 2, you are more likely to feel that the braking is harder when the pressure is low. But in Gen 2, you can be lulled into thinking it feels find, until the moment you want more than you've got.

Some people go straight to opening their wallets, grabbing wrenches, and replacing expensive subsystems. An excellent post from just yesterday demonstrates how you may be able to save a real bundle by not skipping the part where you diagnose the problem.