LED is behaving weirdly even though I did everything that I'm supposed to do.

Hello everyone. I'm completely new to the world of Arduino. I got it yesterday and was trying it out today with the most basic example of blinking an LED. If I use pin 13, the "L" LED blinks. But I've connected another green LED to the pin 13 and the GND. The program is alright since it uploads successfully and says "Done Uploading". I tried using pin 12, but it didn't work either. I am using a 220 ohm resistor too.

Edit: It worked a few times. But then now the "L" LED has dimmed, so has the green LED. Both are blinking weakly. Is that supposed to happen?
Now it shows error messages like this:
Arduino: 1.6.7 (Mac OS X), Board: "Arduino/Genuino Uno"

Sketch uses 1,052 bytes (3%) of program storage space. Maximum is 32,256 bytes.
Global variables use 9 bytes (0%) of dynamic memory, leaving 2,039 bytes for local variables. Maximum is 2,048 bytes.
avrdude: stk500_getsync(): can't communicate with device: resp=0x14
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 3 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 4 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 5 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 6 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 7 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 8 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 9 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 10 of 10: not in sync: resp=0x00
Problem uploading to board. See http://www.arduino.cc/en/Guide/Troubleshooting#upload for suggestions.

This report would have more information with
"Show verbose output during compilation"
enabled in File > Preferences.

Along with that, the "L" LED is constant when the green LED is not connected, and starts blinking weakly again when the green LED is connected. Why is this happening? Please help.

It's all a bit vague. So let's go back to the beginning. Disconnect everything except the USB cable to the computer. Try to upload the unchanged Blink sketch.

Does it upload successful?

Does L blink again?