I have had continual problems with a power steering fluid leak. We have replaced lines and now the pump has gone out. What are the chances that my rack and pinion is broken?

Why are you not taking it to a mechanic?? It needs put on a lift to find the leak.

with power-steering it could be one of three problems. 1- power steering pump could be going out ( normally with the pump the car will whine but will not normally leak and still hold fluid) 2- a leak in your power steering lines ( and can normally be resolved with new lines or sometimes you may be able to bypass and clamp the leak on the line) 3- you may have busted the O rings in your powersteering pump and that will actually cause the pump to leak

hint- alot of people will tell you that you may also use transmission fluid for power-steering this is true you can its that same thing as power-steering fluid just a different color (but dont put power-steering fluid in a transmission, but at the same time if you plan on replacing the pump i would use transmission fluid due to it being cheaper but it will cause the O rings in the power-steering pump to go out quicker to cause a worse leak) so i would recommend to locate the leak first before using trans fluid due to if its in a line you wont have to replace the pump but if its already the pump this is the cheapest fix until repaired

hi Eva.
As you turn your steering wheel it is this fluid pressure that aids in turning the wheels of your car. ... If the pump impeller is trying to move power steering fluid and starts catching air bubbles it can cause whining noises and vibrations to occur.
Maybe you've heard it at a stop light. Maybe you've heard it as you pass a car on the freeway. Or maybe you've heard it in the parking lot at work when someone is leaving. The unmistakable whine of a power steering pump can make even the most confident mechanic wonder when that car will breakdown.
Power steering pump noise is a unique noise that your car may make and once you've heard it you always know what it is. The noise is a mix of a whirring and a whining and will always vary with the speed of your engine whether your car is driving or in park. This whining noise can be subtle or extremely loud and may be worse in colder weather, or right when you first start your car.
Power steering pumps are most often vain style centrifugal pumps that are tasked with pressurizing the power steering fluid and pushing it down to your power steering gear or rack. As you turn your steering wheel it is this fluid pressure that aids in turning the wheels of your car.
There are a few reasons why you are hearing power steering pump noise from your car. First, it may simply be due to the design of the pump. Sometimes, noisy power steering pumps can continue to work flawlessly for years after they start making noise. This may simply be due to the manufacture's design or a tight tolerance in that particular pump. In this case, you would hear the noise but not see any other adverse effect like a loss in power steering, leaking fluid or a wobbly pulley. In this case, you may be able to help reduce your power steering pump noise by choosing a different type of power steering fluid, like a synthetic fluid.
Your power steering pump may also be making noises due to air trapped in the system. If the pump impeller is trying to move power steering fluid and starts catching air bubbles it can cause whining noises and vibrations to occur. Even tiny air bubbles you cannot see that are trapping in the power steering fluid may be causing the whining you are hearing. In this case, the best thing to do is flush your power steering system to try and remove the air from the system. Having air trapped in your power steering system can be difficult to diagnose so you may need to simply try a power steering flush to see if it solves your problem.
Power Steering pump noise may also be due to a failing power steering pump. As the bearings on the impeller go bad it will start to make noise as the pump is turning. If you have a bad power steering pump you usually will also experience leaks from around the pulley, a wobbly pulley, or difficulty turning the steering wheel when you are stopped. If you have multiple of these symptoms together, it is probably time to replace your power steering pump.
Lastly, and most usually, a whining power steering pump is an indication of a low fluid level. Your power steering fluid is probably something you have rarely if ever checked, so it often comes as a surprise if the level is low. Your power steering fluid reservoir is also relatively small so even a slow leak will cause a low fluid level relatively quickly. To confirm this is your problem it is as simple as checking your power steering fluid level. Some power steering reservoirs are clear so you can see through them to check how full they are. You may have to wipe away some dirt and grime to find the "full" line, but it should be easy to check. If you have an opaque power steering fluid reservoir there should be a small dipstick under the cap that will help you measure the fluid level. If it is low, then you have a leak somewhere and topping off the fluid should quite down your power steering pump.
If you discover a power steering leak, rather than simply continuing to add fluid every time it gets low, you should fix the problem permanently so you don't have to continue to check your power steering fluid level. Replacing lines or seals can be a surprisingly difficult task due to the location of your power steering pump and steering gear or rack. The easiest way to seal your leak is to do it from the inside out!

or check this link out for more info on this matter.
Power steering whining sqreeching Google Search

eithor you have blown a power steering hose or the pump itself has gone out on you also check the power steering fluid level make sure its at the full line look for fluid all around the pump signaling a leak

FIRST MECHANICS COULD HAVE TIGHTEN LINE TOO TIGHT AND DAMAGED THE SEAL IN LINE FITTING.TAKE CAR BACK TO FIRST DEALER.LET THEM KNOW POWER STEERING IS STILL LEAKING AND THEY DID NOT FIX THE PROBLEM.THEY SHOULD NOT CHARGE YOU ANYTHING JOB SHOULD BE DONE RIGHT THE FIRST TIME.

Check the fluid level and add if it's low on fluid, look for visible leaks that will need to be addressed. The only other thing to that may have gone bad is the power steering rack and will need to be replaced. Good luck and keep me posted, be glad to know your got your car running 100% again soon.

your seal is probably gone.

The problem could be anything from a power steering hose has leaked out all the power steering fluid or the steering rack could be leaking fluid. Has the car made any strange noises when turning the steering wheel? A car that is loosing power steering fluid will at some point lose so much fluid as to make the power steering pump cavitate (starve for fluid) and the pump will make a high pitched noise when it has too little fluid in it. I can't remember if the 1996 ranger had only one belt on the engine or if the power steering has it own seperate belt. The belt being gone would prevent the power steering from working but if you only have one belt the car would also overheat.

Most likely the power steering pump is your problem. It sounds like the shaft inside the pump has broken and it is not pumping fluid. I would install a new pump and see what happens. The other option would be the rack and pinion (steering gear). The power steering pump is the cheaper of the two and usually the problem. I hope this helps you.