networking - Share wireless Internet connection over the same wireless adapter?

I am currently living in my grandparents' aparatment for a week and I want to get a wi-fi connection in the bedroom. They have a PC with a wired modem (with no routing functionality, a plain modem) connected to it. I put my USB wi-fi dongle into a USB port and set it to AP mode. I can connect to it using my laptop and use the Internet with no problems when I'm in the living room, but when I move to the bedroom, I lose signal. I only need it to watch YouTube videos before I fall asleep, so I had an idea. I thought I could leave the laptop in the living room and use it as a wi-fi repeater, so I can connect to it with my cellphone in the bedroom.

It seems, though, that I can't receive wi-fi signal and share it to other devices using a single wi-fi adapter. But it doesn't seem right to me, there surely has to be a way. (It has to work like an AP - I am using a cellphone which can't connect to Ad-Hoc networks.) I tried an application called mHotspot, which works fine when I try to share the wired connection. But when I try to share the wireless connection, it just freezes for a while and then says: "Hotspot couldn't be started because: The group or resource is not in the correct state to perform the requested operation."

Also, I am using Windows 7 x64.

The question is (TL;DR) - Is there a way to receive and also share Internet connection using a single wi-fi adapter?

Answer

The setup you're looking to achieve (Wi-Fi repeater on a device with only one radio & Wi-Fi interface) is most likely impossible - if not by actual technical limitations (which I'm pretty sure it is), then by limitations in any software you'll likely find designed for Wi-Fi repeating.

To properly work, you'll need a device with two Wi-Fi interfaces which work on two separate radios. Adding a USB Wi-Fi adapter to your laptop might work, given the proper supporting software, but it would just be better to buy a device that's designed for the function.

Generally, it's a bad idea to have a home computer directly exposed to the Internet in the first place (as your grandparents' is right now). So, aside from gaining the ability to provide Wi-Fi service inside the apartment, it's in your grandparents' best interests to just buy a router anyway. (Or you could get one for them.)