Acer Aspire 5734Z-4386 :: Laptop Connects To One Wireless Network But Not Another

First I need to let you know that my home network consist of a Motorola modem/wireless router from my ISP. I have the wireless turned off, then I use a cat5 ethernet cable to connect a Belkin wireless router so that I can use the two USB ports on the back for a Networked storage device for doing regular backups on all the pc's in the house, and my non-wireless printer, so we can print from anyroom of the house, instead of taking the computer back to where the printer is. So about three days ago I got my Aspire 5734Z-4386 laptop, and I did not have a wireless connection. So I checked my phone, and it still had a connection to the Belkin. I took about ten minutes to troubleshoot the Atheros AR5B93 wireless adapter. Could not understand why I didn't have a connection, it was working great about 12 hours before. 
 
So for some reason I used another pc and logged into the Motorola and turned the wireless back on, and immediately the Aspire was showing a connection available, I clicked it and it said "connecting" for a few seconds, and then showed "internet connection". I spent about 5 minutes surfing the internet, and then disconnected from the Motorola and reconnected to the Belkin, it said "connecting" for about a minute, then the yellow triangle came up, no internet. Went back and clikced the Motorola, again internet connection, but not on the Belkin. So I got the other pc and checked the webpage for the Belkin to make sure the Aspire hadn't gotten blacklisted somehow, there's nothing there to explain why I can't connect. So I have spent three days, uninstalling the adapter, and re-installing, I used the Motorola to download the latest driver for the adapter. 
 
When the Aspire is on the Belkin network with the rest of the other pc's, I have no problem moving files from and to the Aspire. I can use the Aspire to log in to any of the other pc's and right-click a file and copy to the Aspire, and watch the file show up on the Aspire, or take the Aspire and copy a file over to another pc, or use another pc to access the Aspire. But I can not get an internet connection, unless I'm on the Motorola network. Now I had the wireless on the Motorola turned off so all the connected devices would be on one network so we can share files, and other network connected activities.