I am surprised this hasn't been said yet, but you need to stabilize and secure your cabinets first. Do it however you like, screws, nails, construction adhesive, whatever, but that has to be secure before anything else. you should be able to stand on it without it moving at all! And the tops of the cabinets must all be absolutely level in both directions on the horizontal. Use shims to solidify the base anywhere that there is a mismatch with the floor. If you use adhesive to secure it to the wall, give it a few days to set properly before moving forward. Once you have a solid base, getting the top to stay in place should be a piece of cake. 100% silicone on top the cabinets, wherever you can, stick it down and leave it alone for 24 hours.