|What exactly is the wireless access point (ie: make/model).|
Chances are it's an 802.11g and can't exceed 54 Mbps. Regardless, the issue is not the network unless your signal strength is really low and the PC is getting disconnected often. The reason I say this is, you say you have a 7 Mbps internet connection so you are limited to, at the VERY best, 7 Mbps. 802.11g is rated for 54 Mbps, you do the math.
Remember, it doesn't matter one bit how fast your network is, or your internet connection is, if the server you're downloading from is very busy. The busier a server gets, the slower it'll be able to service all connected clients.