The only hardware in my circuit is the PIC, an LED, and a 470 ohm resistor.
decoupling capacitors are missing !!!

the " magic " one : 0.1/0.22 µF as close as possible to the supply pins of the Pic , and a " reservoir " one say 100/220 µF in the vicinity ...
add to that ... be sure of your MCLR pin ... ( or to have disabled it ! )

But it's right : These chinese breadboards are pure crap ... ( MCP 47 ... i.e. )

the only one I found quite acceptable is a 40 ( 50 ? ) years old genuine " Lab 500 " one. but not exactly cheap.

Alain