Being that water seeks its own level, you may not be able to fix this issue.
The design of your home is a garage with a basement, the garage foundation walls are only 4 feet tall, while the basement continues to 8 feet down. If you do not already have a way for water to escape underground at the side that is leaking,you may be out of luck.
If there are perimeter drains around the outside, that may be helping a little during lighter rains.
T issue is the exterior wall area from the outside, you need to fix the damproofing of the exterior foundation wall that is under the garage....nearly impossible, or control the water after it comes into the basement with a drain system at the interior.
This is why I tell folks, do not finish your basements with anything organically based. Wood, sheetrock paper and rugs are a sure thing to get mold growing in your home, add some fiberglass insulation that holds air filled mold spores, and you get issues that need to be removed and not reinstalled.
There are companies out there that can help, you need some professional advice in my opinion. try Basement Waterproofing Information and Estimates | Wet Basement Contractors
for further info.