The other way to get to this, is work from the top down. Remove drawer above the refrigerator(if you have one), remove the 6 screws that hold the countertop on, 3 on each side near the top of the refrigerator cabinet. Mine was not easy to take off because the factory set the countertop and wood mounting brackets in wet expaning foam to seal the vent area of the back of the frig. I went this direction when replacing my frig fan at the back of the unit. Then you can get to the next set of screws or stables to get down to the section of wood that needs to be replaced. What I recall the piece of wood you need to replace is stapled in place, you may have to use a hacksaw blade to cut out the staples to remove to broken piece of wood. You may be able to use a alumium angle to sister the broken piece of wood on the back side for your repair. At this point you can get some oak trim and metal angle brackets at a home improvment center to do the repair. Now on my older 97, if I recall, I would have to remove my whole counter top to get to the broken piece of wood. The counter was held in place underneth with screws and metal angle pieces,access though the lower cabinets.
