Rear Brake binding.

Does the piston have a cross pattern on it's face? And is there a pin on the back of the pads? The pin likely needs to fall between the piston spokes, to lock the piston from turning when the parking brake is applied. Even positioning it correctly can be problematic, if the pistons are not well seated before application of parking brake.

do not know if this is your issue, but it will cause terrific drag if it is. So:

1. Position piston correctly, to have it's spoke pattern straddle the pad pin.
2. Reassemble.
3. Pump the brake pedal multiple times, get the whole thing well seated.
4. Reconnect 12 volt battery. (assuming this was done at the outset, should be)
5. Do a short/easy test drive.
6. Apply parking brake when done.

 

I've never seen an 01 with rear calipers. The Gen I's have drums on the rear.

 

Ok, must be a European thing cause all North American models came with drum brakes.

 

Yup. That's a simpler design. And per above, even second gen North American are simple drum brakes. Third gen with rear discs are a flakey, integrated parking brake, no built-in mini-drum brake. When it works it's fine, but assembly is tricky, so not a good design in that regard.

Sorry, not helping with your issue.

 

Here's what we have

 

1. Any warning lights on?
2. If your attempts to depress the caliper piston do not result in a positive change, then is it possible to swap the rear caliper assemblies to see if the problem follows the caliper? If it does, then just replace the entire caliper.
3. If the problem does not follow the caliper then you may have a problem with the brake actuator that provides hydraulic fluid to the brake calipers.
4. The European Classic and 2G Prius both have rear disc brakes (compared to North American and JDM Prius that have rear drum brakes.)