After a heavy rainstorm, water has started to surface through the cement slab separations in the garage. Since the garage is carpeted it dampens the carpet.

I'm guessing, your wanting to stop the water? I would look close at the downspouts and make sure there directing the water away from the garage. Is this something that's just started? Or how long has it been going on? Good luck

Could be a high water table. My garage has 3 feet of #2 stone poured beneath the 10" of cement to promote drainage. On top of that there is a hole in the back corner where we drop a pump to alleviate the dampness.

Water intrusion will happen where the foundation is weak or additional water from downspouts improperly aimed away from the structure occur.