You can install an interior weeping system similar to what you would normally do on the outside, but without the waterproofing.
Start by jackhammering out about two feet of floor around the edges of your garage, as close to the walls as you can get. Dig down until you reach dirt, and if that's not at least two feet down, keep going. Now, put down a couple inches of 3/4" crushed gravel, and then install weeping tile (it's not tile anymore; it's 4-6" corrugated plastic drain pipe with a nylon mesh sock over it). Make sure the sock is continuous across any joins you make in the weeping tile for corners etc. This is a good time to direct those drain holes down into this trench, where the water they drain will flow into the weeping tile. You'll also need a sump, or a connection to a downhill storm sewer; direct the weeping tile to this sump pit or the storm drain. While you're doing all this a center drain can't hurt too much; you can tie it into the weeper wherever it's convenient, just make sure the garage floor and the drain flange are level, or that the garage floor slopes slightly to the drain.
Now, you can install waterproof sheathing on the interior walls contacting the concrete. Normally this product is designed to go outside the foundation walls, but in cases where that's infeasible it can work this way too. The idea is to trap moisture that weeps through the wall behind the sheathing, where it will then be directed down the wall and under the slab to the weeper. So, you'll install the sheathing, which should have an air space between wall and most of the layer, and make sure the end is down in the trench by the weeper.
Backfill the rest of the trench with 3/4" crushed gravel up to the slab footing, then patch the slab with new concrete. Your garage should stay much drier.
This is not going to be the answer you wanted to hear, but here goes.
Although I cannot see the cracks up close, it appears that the cracks were created by the floor flexing in a fairly straight line. The cracks wander in a band about a foot wide with some parallel and joining cracks.
My first plan of attack would be to remove a rectangle of the damaged and weakened concrete apx one foot wide by the length of the crack, apx 10 feet. This can be done with a small hand held jackhammer. ($30 to $40/day at rental store). Slightly bevel the edges back from the surface to create an inverted "V", so it is slightly wider at the bottom than the top. Once the edges are clean of dust and chips, carefully fill the open void with a mixture of concrete mix equivalent to a 5000 pound mix. You can use a ready mixed in a bag, just add water. Keep the mixture a bit to the stiff side, not too wet. Fill the entire void be sure to push the mix tightly against the existing concrete. Wetting the existing concrete isn't a bad idea. Trowel smooth. Done.
The reason I would not recommend a quick fill fix is that there may be lots of other cracks below the surface. If you don't get a good solid patch, water could wick up through cracks or the hidden damage could compress or further separate in future shakes. Although it seems like a big job, a 1 foot by 10 foot removal and repair is not as bad as it sounds. With the proper tools, you should be able to do the whole job in 4 to 6 hours. Good Luck
Best Answer
If you are only interested in thickness of your concrete slab there is a method to measure it. Sometimes when someone doesn't know the strength of some old concrete element which was poured by someone else people hire specialist for this; they use special tool which is cylinder shaped and which drills the concrete and extracts concrete cylinder, which than you can measure. Don’t be afraid that you will damage the slab because it is only inch or two wide. On the other hand if you are wondering what is wrong and how to fix it you need to provide us with more details. People who wrote comments have asked the right questions, especially Ecnerwal.