Q: Can an ink pen falling under the emergency brake cause the brake fluid to heat up and the brakes to fail. The emergency brake work

I took my car to the dealer to get new front brakes, new rotors, tires, and change brake fluid and hoses. On way home, I heard a clicking noise when I put on the brakes but thought it was just the new brakes adjusting. I park the car for two days and then on to work on the third day I smelled something burning. I thought it was something outside the car so I close the vents. The smell stops. About three hours later the smell return so I close the vents again. I went home after work and park the car for another two days. On the third day, again I was on my way to work and was about ten blocks from my home and coming down a hill and put my foot on the brakes and they would not engage. The right wheel begins to pull to the right and I pulled up the emergency brake to stop the car. I took the car back to the dealer who had the car for a week and now is telling me they found an ink pen under the emergency brake that heated up the brake fluid which cause the car brakes not to engage.

My car has 36000 miles.
My car has an automatic transmission.