Check if Arduino Uno connected with PC
You can't determine if there is a valid USB source on the UNO without modifications, because the Atmega328P just receives serial data when the host sends some data. Some approaches that you can keep in mind.


If you want to determine whether you are connected through the USB or barrel connector, you can connect an analog pin to the Vin pin through a voltage divider (you should calculate the values so that you do not exceed 5V on the analog pin). This way if you detect a voltage greater than 6.6V you will know that you are being powered from the barrel jack.
If you want to detect a particular PC, you can write a SW in the PC which scans for new ports, then opens them and sends a particular string. If you receive that within X seconds, you know that you are connected to the PC
If you want to determine if you are connected to any valid PC, then I think you will need to modify the program in the Atmega16u2 which is used as a serial bridge between the two. I'm not sure whether it is possible or not, but I think that the Atmega16u2 knows when a valid USB session is started, and so can tell the Atmega328 this information (through the serial interface)