RE: How thick is the surface?
Depends as much on the nature of the ding as the depth:
Smooth dings (compression dings) without surface fracture could be 3mm deep without effecting the boards waterproof integrity.
On the other hand, a good solid crack (hard boom impact on nose etc) could cause a lot less than 3mm but still create a leaking board.
Check out the board's seal by allowing it to warm moderately on a hot day and then release the air valve (vent screw) - hopefully a small hiss will confirm the board stil remains sealed (note a small amount of soapy water over the vent screw can help give a visual clue there, even if the audible one is not noticeable.
If (instead) water is hissing out the ding holes, well....
if you've any doubt or uncertainty, have the board checked by your dealer,local repair shop or at least an experienced local sailor who can show you first hand how to check it out.
Cheers ~ Ian