Haier HLP23E - When I press start, the water flows in and out at the same time.

Does it drain the water out? It will not move on to next cycle until it has drained fully.

Check to be sure water is cut on and there is actually water coming from hoses. Make sure hot and cold hoses aren’t switch at Machine. Make sure valve and hose screens are free from debris.

the water pump on a washing machine is nothing more that a water stirrer as the vanes are straight out
the pump is full all the time and passes water if the hose is laid on the floor. the fact that it is not pumping indicates that it is not getting power at the right time. or the motor of the pump has malfunctioned O new pump) The over flowing machine indicates that the hose to the pressure switch ( what you turn for the water amount ) is blocked or has a hole in it
With both problems combined it may be a faulty control board so have a washer machine mechanic have a look at it.

check belt and bearings

I would replace the pump impeller first!

Had the same problem w/the water inlet w/initial installation. When the water inlet was hooked to the faucet and into the washer, water leaked on the washer end. The manual tells you to put a new "flat" washer (provided) in the washer machine water inlet, but water still leaked. It's actually the not flat washer, it's more of an "U" shape washer that goes into the washer machine water inlet and fits right over the filter in the water inlet valve. Leak was solved, but faucet was on and water was not filling in the drum. Turn power on, select cycle, water level, and press start and water should start filling the drum.

if its an unbalance fault make sure the machine is level and not wobbly,if all good then you may need to fit a new set of suspension roads,P.S alot of machines have this problem on small loads

tub rubber is torn or cracked can be replaced but for cost u might buy a new washer

Hey rosedunn i have the same problem :( ... So what you do with yours???thansk