I have several,areas of my laminate floor damaged due to water or other various mishaps throughout the years.
These are the methods I have used to repair them.

Step 1: Gather Materials

I use Gouache or water soluble oil paints.
Assorted paint brushes
Water based polyuerathane or mod-podg
Baking soda if filler is needed
Water
Sandpaper (150/220 grit)

Step 2: Sanding

Prep surface sand with 150 grit and block on effected areas

Step 3: Fill

I use Mod-Podg mixed with baking soda until smooth as a filler but wood filler may work just as well.

Step 4: Final Sanding

Sand the filler smooth with 150 grit the sand entire surface with 220 grit.

Step 5: Mix Paint

Mix paints to best match lightest color. Apply to all surfaces sanded. Water down brush and taper blend edges.

Step 6: Add Detail

Mix paint to best match grain and with a fairly dry brush ease on grain marks to match surrounding areas

Step 7: Apply Finish Coat

My surface isn't very glossy. I have applied a Matt base Mod-podg to protect the paint. The glossier the surface the easier it is to see blemishes.
Hope this helps someone in restoring the look of their damaged floors