LED on Pin 13 always blinking

Hello,
I'm new to arduino I have done like 3 or 4 projects. the board worked fine but now I have a problem
when I power the board using USB cable it works fine, but when powered through the battery via DC jack the green light glows little dim and the 'L' LED on the 13th pin starts blinking very fast and the voltage from 5V/any digital output pins is ~1.8V (previously ~5V).

Of course i can program the board the IDE successfully uploads the program to the board but the only problem is i can't use when i connect the battery, only when powered through USB and I have checked that the battery is fully charged (12.37V) and measured the voltage in the Input jack in the board it also measures (12.37V).

Which board are you using?

Do you have anything additional connected to the board?

What type and size of battery have you connected to the board?

Are any parts on the board getting hot, in particukar the regulator, when the battery is connected?

Is the battery voltage still ~12V when it is connected to the board?

I'm using ARDUINO UNO

I didn't connect anything to the board

The battery is a 12V Lithium-Ion (3x4.2V, 2000mAh cells)
Dimension 15.2x10.2x8.9 cm.

yes the voltage regulator is heating and it seems burned, I have attached pics of the regulator ,also in the regulator the output pin gives 1.79V and input to the regulator is 9.08V

the battery voltage is still ~12V when connected.

That is a fried voltage regulator.
Stop trying to use your board before you burn more things downstream.

You can try replacing it
http://www.ebay.com/itm/10X-AMS1117-5-0-5V-LDO-SOT-223-Voltage-Regulator-10Pcs-SHIP-TODAY-New-/181985964500?hash=item2a5f3571d4:g:CjcAAOSw3ydV7WIR

if you know how to solder, and haven't fried anything else on the board.

You COULD keep using the board if you have a trusted, regulated, 5V power source. You can plug that into the 5V pin and GND.

The regulator is well fried!

You have to ask yourself when and how this happened, typically they make a pop, crack or hissing sound and smell bad when they fail :(. It is possible the part was faulty but it is also possible that it has been damaged by reversed power connection at the Vin header pin.

The regulator is pretty tough and tolerates most forms of abuse but not reversed polarity. The input jack has a diode in the power line that protects against reversed connection but that may be blown to a near short circuit if you have been probing the board and accidentally shorted out something (meter on Amps range?), it is certainly suspect as 3V is getting dropped somewhere according to your measurements.

So you will have to use the board on 5V USB (check the regulator stays cool when powered from USB only). Alternatively repair the board by replacing the regulator as already suggested by INTP and replace that suspect diode too.