Well, in general, this problem is usually caused by one of two things - a binding brake pedal or some sort of problem with the master cylinder. Let's check the brake pedal.
The reason why the brake still partly on after releasing the brake pedal.
(1) Binding brake pedal.
(2) Problem with the master cylinder.
Car troubleshooting
Inspect the area around the base of the brake pedal. Check for anything which may be restricting its movement. A brake pedal that is working normally should move without resistance for the first inch or two of travel (after which it will move with resistance, of course, since the brakes are then engaging).
If the brake pedal is binding, an incomplete retraction of the brake pedal is causing brake drag. As indicated, the brake pedal is binding (i.e. it's not fully retracting). So basically, the brake pedal is always "down" somewhat and hence, the brakes are always applied or "on" somewhat.
What to do?
Correct whatever it is which is causing the brake pedal to bind (e.g. bunched up floor carpet). If you can't fix it yourself, take this car to a garage as soon as possible.
But if the brake pedal is not binding, then there is a problem with the master cylinder. What is key about this problem is that, as indicated, not just one but all four brakes are still partly on after releasing the brake pedal. We were not able to establish a binding brake pedal as the culprit. However, it could very well be that there is some sort of problem with the master cylinder. You see, the master cylinder provides the hydraulic pressure that activates each of the four brakes. For some reason, the master cylinder is probably not completely "letting up" on the hydraulic pressure (after the brake pedal is released) thereby causing the brakes to still be somewhat "on".
What to do?
Have a mechanic inspect this vehicle's master cylinder. A few items which you may ask him to check are: master cylinder pushrod out of adjustment, swollen primary piston cup, and blocked bypass port.
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