I've just learned a valuable lesson about running a business; always be two businesses. Then when people phone to try to sort something out because you've screwed them, put them on hold for two hours with intolerable music and then say "oh we can't help you with that, you need (other business that is really the same business), here's their number." Do that with both numbers, and you never even have to actually provide a service at all! For example, be KLM partnered with Delta, or be Delta and deal with bookings done through Expedia, or a be a hotel and deal with bookings done through hotels.com, or even make Walmart and walmart.com have separate phone numbers and blame each other - it's so easy to be incredibly unhelpful!
Make sure to have both customer service and your labyrinthine phone menus (which must never make any difference to who you end up speaking to nor provide them with any information you made the customer enter - the customer service staff must make this clear by asking for all the information again) repeatedly suggest that the customer try to resolve their problem at the website, and when the customer has escaped from the phone menu maze you should also interrupt the hold music every 30 seconds to loudly suggest that the customer should use the website to resolve their problem. For bonus points use a variety of different recorded voices so that the customer can't be sure that someone hasn't picked up this time without devoting all their attention to your timesink - if they can just read a book how are they going to be persuaded not to try again? Do not use a recorded voice to suggest how long it will be before someone will answer - mystery is even more frustrating than lies.
Similarly, if a customer tries to use the website it should suggest that they phone, but not give a phone number unless they first navigate a byzantine 'FAQ' of questions nobody would ever ask, confirming repeatedly that the suggested answers are unhelpful. The phone number at the end should be incorrect. If a customer tries to write a complaint or ask a question with a web form, the site should respond with a vague "failed to send message" error, or, even better, a blank screen so the user doesn't even know that the message won't be delivered. Alternatively, declare that the message has been delivered and will be responded to "shortly". Do not give an approximate time as that will encourage people to try again after that time, and do not actually deliver any message.
Your website should, of course, work just fine up until the point at which you've taken money. The customer should feel secure in making a transaction until it's too late, only then do you refuse to give them a refund because "oh someone else is in charge of that, here's their number."