Sitting right next to the router will not necessarily improve the performance. Wireless signals need space to propagate to their optimal beam shape. Personally, I'd sit no less than 15 feet away from the antenna.
Certainly the proper performance of the one wireless adapter points to problems with the improperly performing adapter. Perhaps it handles interference poorly and there is a 2.4GHz source of interference nearby.
Perhaps you're first step would be to try this same test on someone else's wireless network, preferably one that is in a different physical area than you and has a different brand WAP. E.g. go to a friend's house who has a different branded WAP and who lives in a different neighborhood. If the problem persists, then you can be certain that you need to focus your troubleshooting on the wireless adapter in your laptop. If the problem does not exist, then you need to focus on either your WAP, the RF frequencies in your area or the settings that your wireless card is using to communicate with the WAP.
Once the trouble has been sufficiently narrowed down, more troubleshooting can be performed.