Long post. Skip to the end for my advice.
Civil engineer here, but I don't deal with structures or foundations much. I'll give some very general comments on the basic principles I learned in college.
The design of a building structure and its foundation are completed sequentially, then fine-tuned to work together.
Step One in structural design is to add up the loads on a structure, in this case the garage. These are called design loads. Absent earthquake loads or other extraordinary factors, there are two types of design loads.
Dead loads are the forces exerted as a result of gravity and the mass of the building components acting on each other. The weight cascades from the floors and the roof downward through the walls to the foundation.
In this case, the total dead load of the weight of the building is distributed primarily around the perimeter walls.
The dead load is not transferred uniformly to various locations on the foundation. The magnitude of the load will vary based on the characteristics of structure above. For the back wall and side walls, the dead load on the foundation might be calculated as a relatively uniform X lbs. per linear foot. Where door openings are present, the weight of the structure above a door is transferred via the door header beams to the adjacent walls on either side of the door. So if the total weight transferred to the foundation from the walls is the same on the front as in the back of the garage, then the walls in the front will be transferring X+ lbs. per linear foot to the foundation. In the same load is transferred to a shorter sill plate distance due to the door openings, creating a greater force per linear foot.
Live loads are the second type. They vary from day to day. They include snow, wind, the contents of the building, etc. Building codes will prescribe how a structural engineer should calculate the live loads and various safety factors, but the overall effect is that the calculated building load transferred to the foundation will be bumped up to X++ lbs. per linear foot.
The design load calculations above generally assume the foundation is the Rock of Gibraltar, fixed and immovable.
The foundation design comes next. Since building the Rock of Gibraltar is impractical, the designer's task is to come up with a design that is good enough to support the design loads in an economical, code-complaint fashion.
Whatever the foundation type, the building loads are transferred through the foundation to the earth. So question #1 for the foundation designer is "how strong and stable is the earth at this site?"
I'll skip the details of soil types, but the investigation of the soils will result in a determination of the load-bearing capacity of the different soil layers. Stability can be affected by slopes, soil type (especially expansive clays), ground water characteristics, moisture variations, frost depth and some other factors.
The soil can be modified to alter the factors, but usually is not for a residence. As with the structure above, codes affect how the various strength factors are calculated. The end result is a calculation that says a foundation bearing at Y ft. depth can more or less imitate the the Rock of Gibtaltar at up to Z lbs. per square foot of downward pressure.
The next to last step is to select foundation materials and cross-sections that transfer the wall loads through the foundation to the soil.
The last step is coordinating the connections between the house and the foundation so that the house doesn't slide, lift up or topple when wind exerts a sideways shearing force parallel to the ground.
(I've just summarized about 12 semester hours into a few paragraphs. There's more to each step in a real design.)
I say all of that to give the OP the background on the order to troubleshoot the source of the problem.
First, eliminate changes to the structure's dead load as a cause. Too many layers of shingles? Several grand pianos stored in the attic? Doors added, creating greater wall loads per linear foot?
Next, think about whether there have been changes to the soil conditions around and under the foundation. The likely suspects all fall into the category of water being bad for soil strength and stability. Did the gutters and downspouts get removed? Did the water table rise? Did grading around the foundation hinder water's ability to get away from the foundation?
If changes to the loads from above and changes the soil's bearing capacity below can be eliminated as root causes, then you pretty much know that you either have an inferior foundation design or deterioration in the foundation materials is the root problem. Given the age of the house, deterioration is the leading suspect.
I'm with Sunset. Hire a neighborhood kid or a day laborer and start digging around to see parts of the foundation. You should know what has failed and why before making decisions on whether to replace or repair the original design.
No doubt a continuous prosperity, though spendthrift, is preferable to an economy thriftily moral, though lean. Nevertheless, that prosperity would seem more soundly shored if, by a saving grace, more of us had the grace to save.
Life Magazine editorial, 1956