Our coffee maker broke so I took it apart, identified the problem and called the manufacturer to order parts. After the "did you check this, did you check this" spiel I told them exactly what I found wrong with it and they sent me a new one. I am writing up the function of the coffee maker for a technical writing report.
Originally I had identified the problem as what I thought were pumps, but I stopped there and did not investigate if the problem was electrical or mechanical.
As it turns out these are not pumps, but rather solenoid operated valves. There are two of them, one to allow water to flow into the heating chamber, and one for overflow into the catch tray.
The problems were that when it was time to brew coffee the valve connected to the water reservoir would allow air to bubble up through it creating insufficient pressure in the heating pot to force hot water through the k-cup. The other valve was not sealing and allowing water to dump into the overflow.
Here is the valve and inside of the housing.
And this is what was caught between the valve and housing keeping it from closing. You can not distinguish it in the picture, but there is a silicone gasket that creates the seal between the valve housing and the solenoid coil. I believe that this was a piece left from the creation of that gasket.
After removing the unwanted material I also stretched the spring out a little in both valves.
Both problems seem to be fixed, and I feel a little bad because now I have two working coffee makers, but I did accurately describe the problem to the company so far as I knew at the time, and they made their decision. I had called to order parts, and they told me to keep the old one for parts :)