Optiplex GX400 keeps loosing internet access

Have an Optiplex GX400 running XP Pro with SMC 2802W wireless PCI Card and SMC 2804WBR wireless router.  XP Pro is set up for multiple users.  Computer connects to Internet fine when first booted and continues to work OK for initial session.  If I go away and come back sometime later, or if a different user logins in sometime later, the computer may or may not be able to access the internet.  When I loose the ability to access the Internet, the icon in the system tray still shows a good wireless connection with a strong signal.  But if I try to ping Google or Yahoo, the packets get lost.

 

Other computers (e.g., Inspiron 4150) can still access the Internet through the SMC 2804WBR, so I don't think it is a problem with the router or my cable modem.  Rebooting the GX400 temporarily solves the problem.  That is, I get back to where I started the story.

 

The GX400 has the latest bios available from Dell (A05) and I have run enable_s3.reg from Dell that supposedly adds some registry entries for dealing with an XP S3 sleep state issue.  I have also reverted to version 6.1.744 of the ZoneAlarm firewall because later versions were reputed to cause the type of problem I am experiencing.  I don't believe ZA is the problem at this point because the inability to access the internet persists even if I turn ZA off.

 

Any idea what is causing this and how I can fix it?