Arduino Uno won't upload code and overheats
The fact that it doesn't blink the LED when plugged in or reset indicates that the bootloader of the main microcontroller no longer works.
The fact that the computer no longer recognizes the board as a serial port means that the USB-to-Serial interface doesn't work.
The fact that it heats up tells you that at least one of the chips on the board is dead.

I'm afraid that you'll have to get yourself a new Arduino.