Recently I started working with a uArm metal that has been stationary for awhile. The uArm Shield is on its way, but I started messing with the arm without it. For a day it worked perfectly, but the next day I lost rotational motion. Thinking that Servo 1 was blown, I tried testing the voltage out of the PCB and checked if the cables were broken but they seem fine. When I tried to switch the places of the servos, seeing if I would get rotational and vertical motion, or rotational and horizontal motion instead to see if it was strictly that one servo that did not work I lost power to the whole arm. I still see it as a device in uArm Client but nothing moves. What servo does the metal run on, if I do in fact need a replacement servo?
It is very important to calibrate the arm before any use. Once calibrated, the information is stored in the uArm EEPROM and does not normally need to be done again. Please note that there are two different calibration methods, one for the learning-mode examples, and a different method for use with the Arduino firmware. Make sure you have used the correct calibration method.
I managed to destroy a servo with improper calibration myself. 
Did you ever see any smoke come out of the servo or notice that they had gotten very hot? If so, those servos are probably dead. You can also check to see if they are locked in a fixed position when power is off. This can also indicate a burned servo.
Without knowing what you were doing with the arm (signals-wise), it is hard to say what may have gone wrong. uFactory used to sell the servos, but I do not see them on the site currently.
They did get very warm. They seem to keep trying to rotate past their maximum rotation and freeze up.
Yes, what you were most likely seeing with the servos was the effect of the servos attempting to move to a position where they mechanically cannot move. The servos will continue to try (and fail) until they burn out (or are shut off).
You may have seen that the UArmForArduino library has safety checks that ensure the programmer cannot accidentally move to an invalid position, for example (0, 0, 0), but this relies on the servos being properly calibrated.
One would not think that the board could be damaged by a burned servo? I am a complete novice on the hardware side of things, however. 