I doubt that it is related to your processor. I have a few old test machines that have N usb adapters and they work fine.
If you mix N and G on anything but the latest routers (with simultaneous dual band) you will only get G speed on all devices. While 54Mbps is the stated speed for G, that's the theoretical maximum and you will not achieve that with real data transfers due to network overhead and signal loss.
N and G both use the 2.4GHz frequency band, and N uses MIMO (multiple input multiple output) and wider channels (40MHz instead of overlapping 22MHz) along with aggregating frames to allow a higher maximum data rate. N can also use the 5GHz frequency band and that is very useful to keep your speeds up -- if you also have older G devices the N network will default to the slower G speeds. One way to avoid that is to have one of the newer routers that provides for simultaneous dual band use, so the N devices can operate at higher speed on 5GHz while the slower G devices use the 2.4GHz band. Of course your N network adapter has to also support 5GHz to benefit from that.
One other thing is that G wireless only has three non-overlapping channels: 1, 6, and 11. All of the other channels have some overlap. Almost every router should allow you to change your channel to avoid interference from other nearby networks. Unfortunately, lots of other stuff also causes interference at 2.4GHz: cordless phones, baby monitors, microwave ovens, wireless speakers and headphones. Also the physical layout of the rooms and distance to the router will affect your signal.
To use WPA2, preferably with AES encryption, you must have both the network adapter and router supporting and configured to use WPA2/AES. If you use other security it limits your network speed to a 54Mbps maximum speed limit.