Nothing Simple Is Ever Easy
To make a long story short (mainly because there are too many details to remember), my new computer is toast. Everything the support techs had me do over the phone didn't work. We can send tech support to your house for free, they told me -- as long as I bought a $200 warranty. When I asked if I could take the computer back to the store to get it replaced, they suddenly remembered the free option: they shipped me a box and prepaid shipping label, and I would send the machine back to them. I dropped off the box at the package service's warehouse last week (and made sure to get a receipt). Now it's a matter of "wait and see".