If they are not responding to emails or calling back - then yes - contact their customer. But I would call once again and let them know if you don't hear back from them today - their customer will be YOUR next call. If still no response - rebill the invoice to the customer with a note explaining the non compliance of your customer and your numerous attempts to secure payment.
That usually gets a response....
Send in a complaint to Load Link also - from the previous posts noted below - seems like you aren't the only one having difficulties getting paid.
Good Luck