Got a money limit in mind? My previous laptop was from eBay, though I know you said that's out, it was quite reasonably priced, and still had 6 months of Dell "Gold" coverage. That got me a new motherboard, btw (with in-home service), because a minor connection through the board wasn't working after 5 months.
I'm only saying this because you might want to research that particular laptop. It was a Dell Latitude - as they called it, "the darling of traveling salespeople" - and it was an excellent machine, imo. It was basic, light, reliable, and affordable. Apparently, many companies use them for a few years, then sell them... sort of like a "company car."