Paul__B:
It certainly sounds as if there is a problem in the wiring.Some photos (must be perfectly focused) would be to the point.
Note that the wiring of that relay board is tricky. You connect "GND" to the relay supply, not the Arduino. "JD-VCC" (without the jumper) goes to the 5V powering the relays. "VCC" goes to the Arduino Vcc and the control inputs go to pins on the Arduino which are active LOW.
Specifically, you do not connect the Arduino ground to the relay supply ground; if you do the opto-isolators are meaningless.
FOCUSED pictures are important.
as for the relay board, it appears that it is one that does not allow separation of ground. there is only one ground connection, one Vcc connection and then the 4 signal inputs.
I did not find the data sheet or schematic that would show the use of the jumper.