The starting price for the Mac Mini went from $599 to $799. Future Publishing via Getty Images Apple's Mac Mini starting price rose this week as the company reported a surge in demand. The cheapest model is now $799, and the $599 model no longer appears on Apple's website. CEO Tim Cook says AI is driving the unexpected demand for the device. Apple's "most affordable Mac" just got more expensive. The starting price for the Mac Mini jumped $200 this week as the company reported an AI-fueled increase in demand for the compact computer. The $599 base model with 256GB of storage, touted on the website as the "mini-est, most affordable Mac with mighty performance," had disappeared from Apple's site as of Friday. The website now says the starting price for a Mac Mini is $799, which comes with 512GB of storage. Earlier this week, the website listed the starting price as $599, the Internet Archive shows.…