Ok, by the time I wrote this post, I came back home and gave it another shot, and found a solution. It's very non-scientific, but I've been able to reproduce it, even if I don't understand the technicalities behind it. So... here's the solution that worked with me: the receiver was powered on, but the input selection was on HDMI2, while my laptop cable is on HDMI3. With the receiver in that state, I plugged the cable in the laptop. Since I have Windows 7, it remembers my settings and as a result, my laptop's screen went black, because my settings tells it to go black. And only then did I position the receiver on HDMI3; I could see my desktop on the TV, went in the display settings, and voila! The 1920x1080 option was there, and it was even "recommended". Selected it, and the TV is now displaying Windows at that resolution.