What is the model number?

Sounds like a power problem to me.
Check the power to the unit with a meter.

Try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker.
Check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
Do this with the heater off and on.
[COLOR="Red"]Be careful as 240 volts is lethal !!![/COLOR]

What I think is happening is that you are missing half the line re: the L1 side. When you hold the dryer start you are creating an alternate path for the good side of the line and that is then powering up the washer fill valve.

Another thing to check is if the unit is wired correctly. re: it is wired for 3 wire and you are using 4 wire or the opposite. You should be able to find this in a manual online either an install or an operators manual.