3.3V pin, Arduino UNO R3, doesn't work!

Which USB to TTL serial chip does your Uno have? On some of the Uno derivatives, they used a pin on the CH340 to provide 3.3 V to the 3.3V pin.

From my reading of the CH340 datasheet, that seems to be not a usage intended by the designers of the chip. It's possible that pin is not as well protected as a dedicated voltage regulator would be and it could have been damaged by you subjecting that pin to conditions outside its rated specs. Of course it's also possible the board is defective and the 3.3V pin never worked.

If you have an official Uno or a faithful clone then there is a dedicated 3.3 V regulator (LP2985-33DBVR), which is shown on the schematics and Eagle files available from the "Documentation" tab of the product page: