If you have really bled everything, and get solid fluid (no air) out the caliper bleeders, then the master cylinder is either defective, or was not 'bench primed' to get the air out of it.

If you need to bench bleed it, you will need a bleeding kit. Most master cylinders come with them. It would be two plastic fittings, male pipe to hose bib and two short tubes. Screw fittings into master cylinder, after removing the brake lines, and run the tubes back into their respective reservoirs keeping the ends submerged.

Gently pump the brakes 5-10 times or until no air comes out of the submerged tubes.

Then bleed the brakes again, starting with the longest run from the master cylinder to the shortest.

Or, have it towed to the shop.

Good Luck!

I personally find that accidental swapping of the front brakes is most unlikely......and even if possible, that would not cause the problems you are having......

I tend to agree with another poster, either the master cylinder has got unpurged air or it is defective......assuming that no oil leaks out onto the floor, or into the inlet manifold (start engine and look at the exhaust color, though a cat makes that more difficult to see!)

As an easy test, open the rear wheel cylinder furthest from the master. Open the bleeder, and have an assistant push the brake pedal to the floor. There should be a solid stream of brake fluid coming out of the open bleeder. If not you have air somewhere, a bad master, or a master that is not allowed to return all the way, thus not being able to sake another drink of fluid from the reservoir. You might try loosening the master from the booster by 2 complete turns of the master cylinder mounting nuts.

If you place your finger over the open bleeder, you can safely allow the pedal to return for another stroke of the master.

This is a test only. Use a pressure bleeder until you are certain you can bleed properly. Good luck.

This is a repeat of a answer I gave a while back:

They have a tool for "bench bleeding the master cylinder, you would be surprised at how many techs do not bother to bench bleed the master cylinder correctly or the they don't know how. I work for a remanufacter of auto parts, Brakes being division that I work at.

http://cardone.com/English/Club/Service_Plus/10908BBF%20bench%20bleeder%20flyer.pdf

there's a link at the bottom of the pdf that shows a video clip for bleeding the cylinder

Hope this helps

Jim C

One simple trick that helps with getting latent air out of a master cylinder is to "feather" the brake pedal lightly with your hand.

Have an assistant look for air bubbles floating up from the pistons as you do this.

And NEVER EVER LET THE MASTER RUN DRY!!!!

This will cause you more aggravation than you need in a lifetime.

Reversing the calipers is a difficult task, and will usually not leave enough hose for the wheel to turn, or the banjo bolt to even be attached.

As long as the bleeder (top) is above the level of the banjo bolt (bottom), it should bleed all the air out of the caliper reservoir.

I just did front calipers on a Subaru, and they are made so well, they were air free from gravity bleeding. And, to error on the side of caution, I normally change the brake hoses when I change a caliper, in case the hose collapsing was part of the cause of caliper failure. They can, and do collapse, and will trap fluid in the caliper, even causing a brand new one to "hang up".