There are too many unknowns to answer this question. What type of soil is there so a reasonable active pressure, passive pressure, and sliding resistance can be determined? What surcharge is on the 7" slab? How far from the face of slope is the wall located? What is the frost depth? What type of masonry? Grout? Mortar? Reinforcing?
This wall is high enough that a building permit and engineering is required. Do not attempt to design it yourself. Without all the answers to the above questions, I already know whoever drew the detail is not qualified. The vertical reinforcing is too far apart, and it all should be located on the tension face (soil side) of the wall. There is also a need for horizontal reinforcing in the wall, and vertical and horizontal reinforcing in the footing key. Sorry, but spend the extra bucks to get it designed right.
It's quite hard to tell how big this wall is but you stated it's 3-4' tall.
It looks like it was built simply as a vertical wall. There's nothing you can do about it. It was inevitably going to tip over. So yes, you do have to dig it out.
If you want to replace it with timber, you need to add something called deadmen to it. A deadman is a timber that runs perpendicular to the wall itself that is then attached to another timber that runs parallel to the wall itself. Diagram:
Without those, your timber wall will always end up getting pushed over eventually.
The catch is, of course, to bury the deadman, you need to excavate all the dirt behind the wall back to about the same depth as the wall...so you'd be moving the 4' of dirt behind the wall as well. That may or may not work depending on who's side of the yard that is.
Another option is to go with a block wall. Retainer block walls are typically staggered backwards as it goes up. You then line the back side with drainable material (river rock) and a drain tile to allow any water building up a route of escape. However you're pushing the limits of most consumer-size retaining wall blocks at 4'.
Yet another option is to build two, 2' walls stepped back (one 2' wall on the bottom, then a second 2' wall several feet behind and above the first one). This is likely the best solution for long term retaining of the land. Plus it may offer some landscaping options (allow you to plant the strip in between with decorative plantings).
Best Answer
That is not unusual in our neighborhood. A sledge will do nothing but break wood. Repairs that have worked are to dig out soil behind the tipped area and replace the vertical posts with longer ( deeper) ones. The larger the concrete "footing" for the vertical posts , the more resistance to tipping. Additional support can be added by driving metal bars into the ground a few feet behind the wall and attach these with steel cables to the vertical posts. The bars and cables will be under the ground surface so not seen , Yes, they will corrode in a few years but by then the soil will have settled down and be stable ( hopefully). I did this with 3/8" steel cable and it was still holding when I moved 5 years later. The digging sounds worse than it is , or contract it.You only need to remove a narrow trench like 2 ft wide and not necessarily all the way to the bottom. An Auger would be a help. I have also seen a new stronger wall built where boundaries permit ; then fill in the narrow gap between the original wall and new wall .