Open the bonnet, turn on the engine. Get someone to turn the steering wheel while you look at the steering shaft as it comes out of the bodywork.
What you are looking for is no play between the steering universal joints and the steering box. The amount that the steering wheel is turned should be the same at the steering rod and the steering box. If travel is lost between there, suspect the universal joints, there are 3 on the steering shaft wiggle each one in turn to feel for play. If this is all ok go on to the next stage.
Jack up the front of the vehicle so the wheels are clear of the ground, get your asistance to turn the steering while you look under and up into the engine bay. What you are looking for is delay in when the steering is turned, and the start of movement in the steering gear. Watch for movement at the steering drop arm ball joint first, then at the track rod ends both sides. Check the panhard rod for movement as well, this could indicate worn bushes.
As stated, your steering problem could be caused by one or more of the above it is a simple case of checking each item in turn.
The steering box can cause symptoms as you describe but this would show up in other ways as well, such as graunching noises and vibration.
I would not atempt to do the crossmember unless you are really competent as it is quite involved.