Compaq Tc1100 Tablet No Longer Connects Wirelessly

My Compaq tc1100 tablet worked perfectly, wirelessly, with our Billion BiPAC 7300NX/N ADSL2+ router, but then it just stopped doing this for no reason that I can think of. In our house is a desktop in each of the 3 bedrooms (one being mine, together with the tablet) that connect perfectly wirelessly to this same router. When I refresh the network list, then one moment it will show my network, and then seconds later when I refresh again, it will give "no networks were found in range".Switching off the router's WLAN security made no difference. Formatting and reloading XP, and installing the tablet's Wireless LAN drivers, made no difference. Moving the tablet around the house made no difference. Now, today I took my tablet with me to spend the day with my wife at her workplace, where there is a Billion wireless router as well (other model). I did not bother to first try to connect with my tablet's wireless card, but instead lent a spare D-Link DWA-125 wireless USB adapter, and connected perfectly. Later in the afternoon, out of curiosity, I started up Xirrus Wi-Fi Inspector, and took a snapshot of it, which is attached here. The whole time I was connected like this, there were, in the bottom right-hand corner, two of those wireless network connection icons, one with a red cross through it.

when removing the D-Link USB adapter --- it was time to come home --- the icon with the red cross disappeared once it was pulled out; I opened IE to see what's happening, and my home page opened successfully. So, was I surfing quite fine with my tablet's own card all day?! I then shut down, switched back on (still with the D-Link removed), opened IE, and my home page appeared again successfully. I did not do any other surfing, I must admit, but just shut down again and came home, where I'm back to square-one with a continual "red-crossed icon".........Using Xirrus here on the home network, and with its "locate adapter" pinger noise thingy enabled, it will alternate between pinging for a while and then keeping quiet --- I can supply the Xirrus 500 sec history snapshot of this, if needed.Yesterday, doing a hard reset of the router *momentarily* gave me "aquiring network address", and then connection, but this soon went away again.The tablet did not have this problem with our previous Netgear router. Nothing's changed in the house: the router and my tablet have always stood where they are. There's no new cordless phones, neither. The one that we have, has always stood centimeters away from the router.

Tablet's ipconfig /all:
Microsoft Windows XP [Version 5.1.2600]
(C) Copyright 1985-2001 Microsoft Corp.
C:Documents and SettingsAdministrator>IPCONFIG /ALL

[code]....