One of the wonderful things about Formica is that it is very durable and designed to take a fair bit of punishment. One of the less wonderful things about Formica is that the very durability it offers also makes restoring Formica very difficult.
There are several products on the market that offer a new sealed and shiny surface after being applied to cover cracks and scratches but you will have to use trial and error to see which one works best with your problem.
Wax Floor Polishes
Many wax floor polishes that will work wonders on floors. A quality floor polish can help restore your Formica.
Clean the Formica
Make sure the Formica is cleaned thoroughly with detergent and water and dried well.
Before applying the polish you can try a wax scratch remover. Scratch removers fill in the cracks so you need to choose one the same color as your Formica. They can be bought from hardware stores. When using them, make sure you apply across the cracks and not along them.
Apply the polish according to the instructions. It is important to use pressure while applying the polish. A rapid circular motion is best. An electric buffing machine can make this task much easier.
The polish will be absorbed by the Formica surface and produce a shine. If the colors of the Formica have faded the wax might make them appear brighter.
These are well sealers and waxes designed for use on counters. These have a cumulative effect and will be well worth using once you have restored your floor.