[BrianG]

Hello. I don't have any experience with BL ESC's, but I do with electronics in general and those caps look bad. See how the tops are rounded? That means the electrolyte has expanded. This can be caused by age (usually 5-10 years, sooner if they are run at very close or just over their rated voltage), running a higher voltage than they are rated, or reversing polarity. The "steam" you saw was probably electrolyte gas escaping.

Capacitors are used to either pass a certain range of frequencies, or to smooth out voltage transients for a more constant current and voltage. I don't know of their function in that circuit, but since they are where the battery wires enter, I would guess they are being used to filter out noise entering the battery wires. They are too small to provide the transient function judging by the amperages the controller will require. Either way, they are needed and that is very likely what is causing your problem.

There are two ratings for a cap: voltage and "farads" usually expressed as uF. All I can see in the picture is 516k0, but on the other side, you should see the ratings I'm talking about. Most electronics shops (RadioShack) should carry those if you feel like replacing them - just be sure they are installed correctly. The white stripe denotes the negative lead.