A broken nfc antenna is unlikely, but to be sure you could inspect it visually and measure the resistance between the pins.
The resistance between the marked pins should be just over 0 Ohms (my 10€ multimeter says 0.5 Ohms).
The resistance between the corresponding pins on the main pcb is about 1.2 kOhms (when the antenna is not connected).
the pins 1+3+4+6 of the 2x3 pin header in the upper right corner are connected, as well as pins 2+5 (in regard to the pinout below). So you just have to measure between one middle and one outer pin.
pinout 2x3 pin header
╔═════════╗
║ 6 5 4 ║
║ 1 2 3 ║
╚═════════╝
all infos only for CC3200 version.