That would, in my opinion, indicate that the 328P is dead. If it's an Uno with a 328P DIL chip, you can replace the chip with a new one (with or without bootloader).
There however might be more damage depending on what went wrong. If your board does NOT have the CH340 serial-to-usb adapter, did you try the loopback test (Loop-Back Test Instructions) to see if that part is still working?
What did you do to the poor thing (that is, what was the project that you were working on when it started failing)?