On your machine someone has disconnected the black wire that goes to the back of the positive Dinse socket, and left it floating. That positive socket should give you the option of plugging in the welding return lead ( "Earth" cable ) at the front, for No-Gas/Flux core operation (Earth positive, torch negative ), or plugging in the flying lead from the torch to make the torch positive for "normal" operation with gas and solid wire.
You have no flying lead from the torch. The thick black wire from the torch, connected at the wirefeed assembly, should be fed back out at the front panel of the machine and should have a male Dinse plug on it. Then you would have the option of fitting that plug into the "+" or the "-" Dinse sockets, making the torch positive or negative. Instead, someone has removed the Dinse plug from that wire, fitted a cable lug, and bolted it to the innermost aluminium plate of the rectifier ( the positive output of the rectifier ). So your torch is always positive, without the option to change over to negative for gasless operation.
To correct this situation and return to having a choice between Gas/No Gas, you need to unbolt the thick black flexible wire ( i.e. the torch wire ) from the innermost aluminium plate of the rectifier, remove the lug, feed that wire out through the front panel, and fit a male Dinse plug. Then bolt the lug at the end of the "floating" black wire to the rectifier plate.
The torch lead is now ( temporarily ) negative, and the positive Dinse socket is now actually connected to the positive output of the rectifier, rather than floating. This gives you the option of putting the welding return lead ( "Earth" cable ) into the positive Dinse socket. So you should be all set up for No-Gas operation....
However, the torch is now negative. I seem to remember that there may be a problem with the trigger switch in this situation. On some Clarke welders there is only one wire in the torch cable for the trigger signal ( on a Euro torch there are two wires, one to each side of the switch contacts ). Pressing the Clarke switch joins that one signal wire to the torch head. Now that the polarity of the torch has been swapped from positive to negative, to cater for flux-core wire, the "torch switch pressed" signal going to the PCB is negative, not positive, and the welder doesn't come on.
This should not be an issue, since with that choice of pos and neg Dinse sockets, this welder is theoretically capable of gas or no-gas operation, but I'm sure there is a thread on this Forum where someone had, and solved, this problem.