1024 is a "magic" number. I say this because:
http://en.wikipedia.org/wiki/1024_(number)
In binary notation, 1024 is represented as 10000000000, making it a simple round number occurring frequently in computer applications.
1024 is the maximum number of computer memory addresses that can be referenced with ten binary switches.
Thus, it's no surprise that in the firmware of the makerbot, that's the max temp value. It also is a safety feature in the firmware that when the extruder controller senses an out of range value on either the thermistor (heated bed) or the thermocouple (extruder) it sets the current sensed temp value to 1024 and then no longer uses the sensed value no matter what, until you reset the extruder controller by pressing the reset button on it (impossible to reach inside the bot) or power cycling (turn off and then back on) the main power supply. The safety feature here is that the heater will never get stuck on, if the sensed temp is 1024 (the max temp) because it's higher than the set temp. This prevents a bad fire, because if the temp sensor just got shorted or disconnected and the temp was assumed low, the heater would be stuck on, getting hotter and hotter until it burns up. This way, the risk of loosing a sensor during operation might fail the print, but save your house.
In short, you have a wiring connection issue and this is pretty common.
I have a custom built Aluminium build surface. I tightened it down just before this started happening.
This could be the source or at least attribute to the problem. A lot of people have had the pin connector on the heated bed PCB rip the copper traces off the board since it's not strain protected. You can attempt to repair but normally it just gets worse and the only option is the $40 replacement. I strongly recommend you get epoxy and put some over the pins and solder joints on the new board to help prevent this in the future.
The bottom line is that the thermistor on the heated bed is not making good connection to the extruder board A6 terminals. There is the wiring harness, the pins and connectors, and the PCB all in that path. They sell bot the PCB and the harness and I would get both as long term spares anyway. At some point, they will break. The wires flex on every move anyway so it's borrowed time. The harness isn't too bad and the board is expensive, but unfortunately, that's how it is. Sorry to hear this but hope you get up and running soon.
Also, I don't see that the caps are swollen so that may not be electrolyte? Not likely the source of this problem The cap closest to the RJ45 is the 12 volt side and the one more towards the center of the board is the 5 volt rail. 12 volt only goes to the heaters (yours is the newer mod board where they leave out the 7805 regulator and use a wire on the bottom side to use the 5 volts from the PC power supply. I personally don't see an advantage but I think they had theories of noise from the 12 volt rail causing issues with the 5 volts stuff. Personally, I have 4 of the boards using the 7805 for 5 volts and never a single problem, even when the 12 volt side is running the heated bed for a reprap which draws some serious power (nearly 10 amps cold or 120watts). Trust me, I can say with no doubt my usage stresses the board and never had a problem. But, there is nothing wrong with the mod they made either.