If the laminate is loose on an edge and heating it doesn't work, carefully lift up the loose area and scrape out the old glue as best you can. Then use a toothpick to spread carpenters glue in a thin layer over the cleaned area and clamp the laminate in place. If you put a piece of wax paper over the cracked edges and then a thin wood block where the clamp tightens down you will prevent damage to wither the top of bottom of the counter.
Before you put a lot of effort into these repairs, it's suggested that you look at replacement cost to see if would make sense. Replacement countertops are not expensive or difficult to install. It makes a tremendous difference in the look and feel of the room.