Atmega328P standalone

Does it (they) work when reinstalled back in the Uno? If so, then it's a wiring issue.

I've wired up plenty of boards just like this, usually without the diode (it keeps any high voltage spikes on the reset from kicking the part into High Voltage (12V) programming mode and looking like its hung).

Check your Rx/Tx, pins, make sure they're not swapped, and that Reset is actually at Vcc.