Bootloader burn problem

I have problem with burning bootloader to Arduino Nano

Burning a new bootloader
Burning bootloader to board 'Arduino Nano w/ ATmega328' using 'USBasp'
Error while burning bootloader.
Burn failed
avrdude: verification error, first mismatch at byte 0x0000
         0x0f != 0x3f
avrdude: verification error; content mismatch

I tried burning bootloader to another Arduino ind it worked OK, so the problem must be in the Arduino Nano.

When i try to upload sketch on it using USBasp, it sayst that upload was successful, but the Ardino seems to do nothing (I uploaded code, that should blink the onboard LED and output to serial:

void setup() {
	pinMode(13, OUTPUT);
	Serial.begin(19200);
}
  void loop() {
	digitalWrite(13, HIGH);
	Serial.println("Blik");
	delay(1000);
	digitalWrite(13, LOW); 
	Serial.println("Blak");
	delay(1000);
}

, but the LED wasn't blinking an there was no printing to serial (Tx LED not blinking))

Attempt to upload it using USB cable had the same effect: upload finished, but the Arduino doesn't do anything.

I think that the Arduino is damaged, but it may be just software problem.

Any ideas?