Finally, at long last, my computer seems to be healed. My deep, but uneducated, suspicion was right--it was actually a virus affecting the wireless router causing the problems. We have several computers that all use the same router when they're in the house. Every computer had issues here in the house, but when the laptops left the house, they were fine. I kept googling "virus in wireless router" and coming up blank because routers don't actually get viruses themselves.
However, this virus gets on your computer and then changes the settings to your router and redirects it to another server...or something like that. So any of the computers could've gotten the virus in the first place and it changed the router, and then we all had problems. Can't recall all the details because I'm not an IT person myself but it has to do with DNS and other geeky acronyms. In any case, I did yet another search, but this time on the Dell tech support forum which I hadn't checked before, and there it was.
So I was right--it was the router all along. My nephew (who is an IT guy) and I took the steps suggested in the forum to fix my router and I haven't had a problem since.
Sadly, that means the second reformatting was completely pointless. Dang. Two days I could've been happily sewing and instead I was babysitting my computer for hours on end while reinstalling. "Enter." (Wait.) "Enter." (Wait.) "Yes." "Accept." "Enter." (W...a...i...t....)