I was soldering Deans connectors to my 11.1V 2600mAh battery and accidentally shorted the connectors for about 2 seconds. It got hot and smelled like burnt plastic. I tested it, and it showed 11.1V, so I continued soldering.

Since I'm new to soldering, the wires got very hot for about 3 minutes. After finishing, I tested the connector, which still showed 11.1V.

However, when I connected it to my ESC, BLDC, and receiver, nothing happened—no receiver light or motor noise. I tested the exposed metal of the connector(While connected to ESC), and it now only supplies 3.1-3.6 volts.

Did I fry my battery, or could the ESC be faulty? (It worked the last time I tested it.)

Do you have a so called LiPo checker that you can connect to the balance connector?
Or else connect it to your charger and do a resistance test or just try to charge it and read the voltages.

But a short moment of a shortcut should not leave the wires for 3 minutes hot, slight chance the shortcut lasted much longer..

Two full seconds is actually quite long for a short circuit - personally, I'd be worried about that battery.

It's possible that you may have burned an internal solder tab and here's an example of how I've made a repair due to a cheap internal solder tab design:

• How to repair LiPo pack