Dennis,
I am an Proffesional installer of Plastic laminate for 35 years and what I do is check to make sure the old laminate is adhered to the wood good and that no sections are loose. You can tap around on the old one with your finger to see if it is still glued down, if it is just sand it with 100 grit sandpaper on your belt sander or vibrate sander to roughin it up a bit. Do this on the edge band also, when appling the contact cement put 2 thin layers with a 100% white china bristle brush on the edge band and allow to dry . Apply your laminate and cut flush and flat with the counter , after that apply 1 thin coat just on the very edge of the new edge band and let dry. When appling contact cement on the rest of the counter you do not need 2 coats, 1 even coat is all you need, do not leave to much where it is goowe or clumpy and do not apply to sparingly. You only need 2 coats on the edge of counter because the new laminate soaks up the first layer of cement and 1 coat is all you need for the rest because your coating over other laminate that cannot soak up the glue. This will work just fine , the only time you may need to remove exsisting laminate is when it is to loose all over the counter, I usually take it all up with a torch when I am istalling custom cove laminate. Do not use a torch unless you know what your doing because you could set something on fire, I have done this so long I don't have problems. If you need any other help feel free to ask. P.S. You can leave your brush in the can of glue to where the glue just covers the bristles and seal it with the lid, it will last for weeks if you keep it sealed when not using .