The pipe was an example only. Do the sockets of your mains electricity supply have an earth pin? If so, use that as the earth connection.
I suggested using a battery as a way of eliminating one possible source of interference which might be the cause of your problem. If the LED operation is ok with a battery supply then the mains power supply is the culprit and will have to be modified for use as a battery replacement. If the LED operation is still erratic with a battery supply then we will need to look elsewhere for the culprit.
Having the probes on one floor and the circuit on another floor is a recipe for disaster. You must use short wires from the probes to the circuit. A screened twisted wire pair would be good. You can, however, have the LED a long way from the rest of the circuit. Ideally the whole circuit should be in a screening box.