I doubt that replacing the vga cable will help. I would agree that your best bet is to get on the phone with customer service, and be persuade them to send you a new one. You should be able to reference the e-mail posted in this thread... if you read portions of it to a CSR and describe the discrepency between their promises and what they delivered, I'd imagine you'd have a pretty compelling case. Remember, when talking with CSRs, if at first you don't succeed... hang up, get a new one, and try, try again.
Also, you may be able to reverse the transaction through your credit card company, if the monitor is basically useless and DOA.
Just because a company notes that a product is refurbished does not give them the right to send you DOA/useless stuff. Quite the opposite, they note that it is often the case that refurbished items are more reliable than new ones... clearly not the case in your example. It would definitely be worthwhile to get on the phone and fight for your money.
I hope not every monitor ended up like this 🙁 Good luck to ya.