Anet A8 reading 739°C from the extruder thermistor!
I had the same issue. Hot-end temperature reading stuck at 209 degrees even with hot-end thermistor disconnected  or swapped with bed thermistor on the Anet A8 mainboard.

After ordering and swapping the AtMega1284p (using jtagice3 and hot-air soldering station) and the 4.7 Kohm resistor (which measured 2.06Kohm on the board and 4.7kohm off the board) to no avail, the only component left in the circuit that could cause the failure was the capacitor.

Swapping the capacitor C47 fixed the stuck reading for me. I used a 10uF instead of a 15uF capacitor as indicated in the schematic. I do not believe it makes much of a difference, and they are much more common. Make sure the capacitor can withstand at least 10V, but I got a 30V one, because the price was similar.

To any body that runs into this issue, before spending time and money swapping components like I did, measure the voltage of the node between R41 and C47 with respect to ground. This is labeled T56 or test point 56. Compare this voltage to T54, T60, T58, and T62 where similar circuits are placed. You should get a voltage of around 5V ( the pull-up voltage) in the functioning circuits, since we are talking about DC voltage, the capacitor should charge up nearly instantly when the the board is powered, and behave as an open-circuit.

In my case, C47 was almost in full short-circuit, and I read a low voltage on T56 ( ~0.5v). 

Since the capacitor was in a low impedance failure mode, the 5V supply voltage of the voltage divider circuit was not enough to power it, hence the fixed temperature readings of the hot-end thermistor ADC channel regardless of the thermistor being connected or not.

Good luck!