How can I repair the wood veneer on a damaged TV console?
You can clean out the debris, carefully salvaging the surface pieces, use filler to adhere the remnants back in position and to make it level where there are missing pieces.  If it is too motley a collection of fragments, just clean out the debris and patch the hole with filler.

Then if you are REALLY artistic, you could carve the woodgrain pattern in any visible filler to match, and paint it to match.  But that will still be noticeable because the texture will be different and you will never get an exact color match.

The alternative would be to patch the hole, then refinish the top, either with paint to make the top uniform (may not hold up to wear) or something like high pressure laminate.

Another option: there are craftsmen who specialize in those kinds of repairs.  They work for the insurance companies or stores and fix damage that happens to furniture when it is delivered or when you move.  That might be expensive.  

You might be able to buy a new top from the manufacturer.  That kind of furniture is usually assembled without glue, so you should be able to remove the old top and reassemble it with the new one.

If you can live with the dent (aren't too bothered by the appearance or can just cover it with one of the things you would put on top), the simple solution is just to stabilize it so it doesn't get worse.  Find a marker of a close color and color the exposed material (hard to tell whether it's wood or MDF).  Then use some glue that dries crystal clear (like the clear glue from Weldbond).  Put a little on a cotton swab and cover the dented area.  It will end up glossier than the rest of the top, but it will keep the broken pieces from disintegrating and rough edges from being chipped.