This is a complicated question. The short answer is yes, there are things the customer can do. It seems like the customer has gone above and beyond the call trying to contact the company, so they're going to have to try other channels. Even while they're doing this, they can submit the claim forms the computer company is asking for and jump through all the hoops. The company might reimburse the customer in the end.
First, if the customer bought from a vendor off Amazon.com or a similar site, they should check out the terms and conditions of purchasing and shipping. The site might be able to help the customer get a refund or replacement through the vendor. Plus, the customer can rate the seller low and leave a comment online.
Next, the customer could contact the company that shipped the computer—if it was an outside contractor, such as UPS or FedEx. The customer could try explaining what happened, on the off chance the computer was broken during delivery. They could ask if it was insured. If they're lucky, the shipping company might have a phone number or email for the computer manufacturer that they haven't tried.
Then the customer could file a complaint with their state's Better Business Bureau, who can warn others to be wary of this company.
If the customer is still not satisfied, and determined to be compensated, they could consult with an attorney. An initial consultation is usually free, and the attorney can advise whether it's worth the customer's money and time to pursue litigation.
Finally, the customer can share their experience on social media. Sometimes this evokes a quick response from companies that do not want their reputation smeared.