I have an HP 4510s with networking problems. So far I have tried 2 different internal wireless cards and 3 different USB devices but none seem to want to connect. My OS is Windows 7 x64 and I have to admit that I haven't tried any other operating systems yet. To sum it up; Windows sees network SSID's, makes an attempt to connect, waits a long time, then fails with the message: Windows was unable to connect to [*SSID*] and this happens with every router I try. This is kind of bugging me because it defeats the whole purpose of having a laptop as the only way of connecting it to the internet is via LAN.
Homegroup is irrelevant at the stage where the laptop can't even connect to the hub. In my opinion Homegroup is irrelevant anyway and it's better to stick to conventional networking.
On to the actual problem - did you you try to connect to one of the routers after clearing security out completely? Do that and only connect for a few seconds - beyond that it could be risky but it would tell that the problem lies in the security so then set a WPA2 security key with ten mixed alpha-numeric characters and be sure to use the same ones when you set up the connection in the laptop.