Budvar10:
The bootloader has no impact to the problem. The bootloader resides in the ATmega2560 chip and it serve programming via serial port on ATmega2560. On-board USB/serial transceiver is ATmega16U2 (if genuine). No activity on Tx/Rx LEDs or better no successful loopback test means that no data can reach the ATmega2560's serial port. Things which can affect this are: driver on PC, USB cable, HW problem with USB/serial circuit, SW problem (if genuine Arduino - ATmega16U2 has firmware which can be corrupted).
You can program the Mega via ISP. It is not only for bootloading. The bootloader is just normal program as sketch is also.
The bootloader burn test was intended to rule out some of the problems. Seems like it's a HW problem with the USB/serial circuit given all the information (I ruled out the USB cable because I have two of them and they both work fine with other hardware).
Anyway, you said:
"You can program the Mega via ISP. It is not only for bootloading. The bootloader is just normal program as sketch is also."
I must be missing something - how exactly do you do this in the Arduino IDE? Or do I have to use avrdude manually instead?