Thanks for the suggestions. It was _indeed_ the master brake cylinder.
Can someone explain how come the car would actually accelerate because of this? I'm pretty sure that it was not just squishy brakes when I pressed on the pedal.
Now for a boring tale of shady mechanics...
I initially took it to my local mechanic, who found nothing wrong _and_ did a safety inspection, but whom I suspect is incompetent.
So on Monday I took it to Tysons Ford in Tysons Corner, Virginia (a big suburb of Washington, DC). I knew that I would pay more for labor, but I figured that a Ford dealer would know Fords.
They had a mechanic check it, supposedly checking the brakes. They "found nothing wrong." I then suggested (based upon the response here) that they check the master brake cylinder. They checked that and "found nothing wrong." That used up my first hour of diagnosis. $85 right there.
They then asked permission to do another hour's worth of checking for another $85. Considering that the car was dangerous to drive, I agreed. The next day they called and said--surprise!--they found out that the master brake cylinder needed replacing. That, along with the two hours of checking, would be $500. In addition, the rear brakes were shot (cylinder locked up, ate up the pads, etc.) and the front brakes were marginal. All total, they wanted $1300 for the repairs.
Now considering that they found none of these problems after the first hour of checking and after I suggested looking at the master brake cylinder, I was highly suspicious. It struck me as if they got me to agree to more labor by lying to me. I agreed to the brake cylinder repair. But two minutes later they called me back to say that they could not do that without an additional $200 of repairs. Every indication I had was that they simply wanted to rook me for additional labor. So at that point I declined all repairs and told them I would pick up the car.
I picked up the car this morning and, lo and behold, not only were they charging me for two hours of diagnostic checks, but they also added $30 for "shop supplies for vehicle repair" for a vehicle that had not been repaired.
So I complained and they immediately started wiping charges off the bill to the point where the manager ultimately told me there would be no charge at all. He even conceded that, based upon my description, the brake cylinder problem should have been obvious.
I then took it to Midas and got the brake cylinder replaced and had them inspect the brakes. They found the problem with the rear brakes immediately, when it had supposedly eluded the dealer's mechanic in his first hour of checking.
I could say that I've learned a valuable lesson in all this. But I've learned this lesson in the past too. How does one ultimately find an honest, competent mechanic?
DDAY