No cold water going into machine
Have a top loader washing machine
Brand ; Simpson Eziset 6kg Simple Wash.
The hot water works only while washing No cold water does
Check that the cold water tap for the washer is turned on and also that water is available from the tap.
Check that the filter in the end of the cold water inlet hose connection into the washing machine is not blocked.
If all of the above are OK then perhaps the machine's cold water inlet valve is either faulty or not being operated by the control board.
If you have a DMM (Digital MultiMeter) you can use its' Ohmmeter function to test that the valve's operating coil is OK. Do this with the power removed from the washer.
Here is a link to a video that in principle shows what to do. (This is not your valve being shown tested).
Hopefully this is of some help.
A multimeter will check for electrical resistance, however inlet valves do have a mechanical component, that sometimes will simply seize, open, closed or in between.
In your case, its likely it's seized closed. It will need to be replaced. Its pretty simple, and the parts is about AUD$20.