New ATmega328

Hard to say for sure.
I missed that you had an Uno - that has 2 ATMega chips in it as well as seperate 5v and 3.3V regulators, vs an FTDI chip creating the 3.3V. So you may be okay on the regulators, you may have purchased a 328P with bootloader, but still be dead in the water for comm's with the PC if the 2nd ATMega part is dead.

I don't have an Uno. You could try connecting via USB cable to your PC, see if the PC says you have a USB device out there, that would be a pretty good indication the 2nd ATMega survived.