What I am wondering is can I send a signal from my computer to the Arduino and have an LED light up? Preferably through the USB port.
This is very easy to do and I wouldn't be surprised if you could find examples of serial port handling that already do what you need.
When the Arduino is connected by USB the Arduino USB drivers create a virtual serial port on the PC which can be opened by any application to read from and write to the Arduino. At the Arduino side your sketch just needs to call Serial.begin() to open the serial port and then read commands from it and turn LEDs on and off accordingly. On the Arduino side this only needs a dozen lines of code. On the PC side you just need an application which can open the serial port and write commands to it. It is up to you to define the command syntax, but for something this simple you could, for example, just send a single byte command such as ascii '1', '2', '3', '4' to turn the specified LED on and '0' to turn it off again.