96 Corsica front right brake caliper locks up with engine running and brake pedal pushed. Releases when bled. Won't lock with engine off. ABS??

Try bleeding some brake fluid on that side. You may have a blockage. Also check if the rotor is in good condition, it may be warped. Good luck!

Have you replaced the caliper and the flex hose ?
How do you get it to release ?

what is the year ,make and model.? does it have abs brakes

If the pads are being applied and you are not pushing on the pedal, it could be something going on with the ABS.

The brake system bleeding procedure differs for ABS and non-ABS vehicles. The following procedure pertains only to non-ABS vehicles. For details on bleeding ABS equipped vehicles, refer to the ABS procedures later in this section.

WARNING Make sure the master cylinder contains clean DOT 3 brake fluid at all times during the procedure.

1. The master cylinder must be bled first if it is suspected of containing air. Bleed the master cylinder as follows:
   1. Position a container under the master cylinder to catch the brake fluid.
   2. Loosen the left front brake line (front upper port) at the master cylinder and allow the fluid to flow from the front port.
   3. Connect the line and tighten to 24 ft. lbs. (32 Nm).
   4. Have an assistant depress the brake pedal slowly one time and hold it down, while you loosen the front line to expel air from the master cylinder. Tighten the line, then release the brake pedal. Repeat until all air is removed from the master cylinder.
   5. Tighten the brake line to 24 ft. lbs. (32 Nm) when finished.
   6. Repeat these steps for the right front brake line (rear upper port) at the master cylinder.
      

WARNING Do not allow brake fluid to spill on or come in contact with the vehicle' finish, as it will remove the paint. In case of a spill, immediately flush the area with water.

1. If a single line or fitting was the only hydraulic line disconnected, then only the caliper(s) or wheel cylinder(s) affected by that line must be bled. If the master cylinder required bleeding, then all calipers and wheel cylinders must be bled in the proper sequence:
   1. Right rear
   2. Left front
   3. Left rear
   4. Right front
2. Bleed the individual calipers or wheel cylinders as follows:
   1. Place a suitable wrench over the bleeder screw and attach a clear plastic hose over the screw end.
   2. Submerge the other end in a transparent container of brake fluid.
   3. Loosen the bleed screw, then have an assistant apply the brake pedal slowly and hold it down. Close the bleed screw, then release the brake pedal. Repeat the sequence until all air is expelled from the caliper or cylinder.
   4. When finished, tighten the bleed screw to 97 inch lbs. (11 Nm) for the front, or 66 inch lbs. (7.5 Nm) for the rear.
3. Check the pedal for a hard feeling with the engine not running. If the pedal is soft, repeat the bleeding procedure until a firm pedal is obtained.

Fig. 1: Loosen the front brake line in order to bleed the master cylinder

Fig. 2: Connect a bleed hose from the bleed valve on the front caliper to a jar of brake fluid

Fig. 3: Always follow the lettered sequence when bleeding the hydraulic brake system

Hope this helps to solve it; remember to rate this answer.

The pedal goes down a long way(Rear brake shoes out of adjustment) or the pedal is hard to push and you have to about use two feet to stop the truck? (booster problem)

your power brake booster is blown out
the seal has a leak in it
run the truck for 3 minutes and shut it off. with the windows up listen carefully while you gently apply the brakes
listen for a hissing sound of air leaking.
the sound of these leaking is a very soft sound

CHECK TO MAKE SURE WITH CAR RUNNING VOLTAGE AT THE BATTERY SHOULD BE 13.5 VOLTS TO 14.5 VOLTS. USE A DIGITAL VOLT METER TO CHECK VOLTS AT BATTERY. WITH ENGINE OFF BATTERY VOLTAGE SHOULD BE 12.5 VOLTS. IF NOT ALTERNATOR NOT CHARGING BATTERY.THAT WILL MAKE ABS AND BRAKE LIGHTS COME ON AND A FAULTY BRAKE LIGHT SWITCH WILL ALSO CAUSE ABS AND BRAKE LIGHTS COME ON.IF ALL LOOKS GOOD.HAVE THE ABS BRAKES SCANNED.IN THIS CASE YOU ARE HAVING BRAKE FAILURE.BECAUSE WHEN BRAKE LIGHT COMES ON THATS WARNING BRAKE FAILURE BECAUSE THE BRAKE MASTER CYLINDER AND ABS UNIT IS TOGETHER AS ONE.NOT SAFE TO DRIVE.COULD LOSE BRAKE CONTROL AT ANY TIME TOW IT IN.

I have a Chrysler sebring 2004, the ABS and traction control light has come on the dashboard display plus I have now no heater. I think it is a blown fuse but not sure

It also sounds like a more likely problem is a seized caliper on the left side. If a caliper seizes, the braking system transfers the pedal pressure to the other caliper thus, the working caliper locks up. Pull both front wheels and look carefully at the wear on the pads. Both wheels should have the same amount of wear. If one side is worn more than the other, the side with the least wear is seized and needs to be changed.
Never heard of a hydraulic repostioning valve, but maybe with ABS there is one. I do know of a proportioning valve which apportions brake pressure front to back and also blocks braking to front or back in the event of brake line failure. Maybe see which he is talking about, should be able to explain the difference. Hope this helps.