How do I get the party that damaged my legally parked vehicle to answer my calls

You need to find out the name of the company that owns the billboard (usually shown right on the board at the bottom).  Search for their address and send them a demand letter asking for payment of your damages within 30 days or something like that.  They should submit your claim to their insurance company who will contact you regarding payment of the claim.  If not, you can file a lawsuit for property damage against the company to collect.