Very good Wi-Fi signal, but no internet access

Hello,
I have a NeufBox NB4-FXC-r2 connected to a LDLC PC running XP SP3 and, at the other end of the house, my wife, in her office, with a LDLC laptop that is somewhat connected to the Box's Wi-Fi. The signal strength was between 1 to 2 bars, sometimes with no connection at all. After researching online, I ended up buying a TrendNet TEW-736RE signal amplifier. TrendNet's technical support being completely useless (they couldn't get me connected!), they suggested I return the device for an exchange. For a day or two, I fiddled with the system and finally got, in my wife's office, 5 out of 5 bars, which proves that it wasn't the device that was at fault. But here's the thing, there was no Internet access anymore.
So if you are for household peace, and if you have a solution that works, you will be a thousand times thanked!

Here are the steps taken:

First step: Securing the system with WPA2 protection. Easy on the PC connected to the box, just go to 192.168.1.1 and go to the Wi-Fi tab, under Security. Much trickier for the remote computer: Start - Settings - Control Panel - Network Connections - Right-click on Local Area Connection - Local Area Connection Properties - Internet Protocol (TCP/IP) - Internet Protocol Properties - Set everything to automatic.
Start Menu, - Run - enter the command "services.msc". You get the list of all local services. Look for "Wireless Auto Configuration". Verify that it is set to "Automatic".
Back to Control Panel - Network Connections - Wireless Network Connection - Wireless Network Connection Status - Wireless Network Connection Properties - Check "Use Windows to configure my wireless network" - View wireless networks. If there are several, use "Move Up" or "Move Down" to put the Trendnet network at the top and highlight the line. Click on Trendnet 736 Properties
Association tab - Check "Connect even if the network is not broadcasting its name".
Wireless network key:
Network authentication: WPA2 - Data encryption AES.
To complete the process, press the button on the box and then the button on the Trendnet.
After all that, I should have been able to connect the laptop to the Internet. But the device is resisting.
Did I forget or do something wrong?

Second step: I followed the instructions to the letter from:
http://forum.telecharger.01net.com/forum/high-tech/INTERNET/Internet/connexion-internet-resolu-sujet_19026_1.htm
which seemed very relevant to me. Still nothing: I tried again: I gave up and am now asking for your help. So, still no Internet on my wife's laptop.

Additionally, I noticed anomalies that I didn't have before:
1) DiskAid, on my PC, used for transfers with my iPad, tells me "The web page is not available because you are offline", which is false, of course. I uninstalled DiskAid and reinstalled it. The problem persists.
2) On my iPad, wanting to send a document from QuickOffice Pro to my PC, I enter the recommended address in Firefox and receive the message "Firefox can't find the server at address 192.168.1.55.4242."

So if you have any suggestions for me, they will be welcome, especially since I've been struggling for a week now, like Aboville, but he knew where he was and I am lost.

Thanks again.