I am having the exact same problem with similar hardware.  I have an Inspiron 8500 w/ Dell TrueMobile 1300 and a Linksys BEFW11S4 v4 with firmware version 1.5.  The problem seems be be related to WPA encryption and SSID broadcast.  Using WEP and SSID broadcast disabled, I have no problems at all.  When I switch over to WPA, I get a connection for a few seconds, then it is gone.  As soon as I re-enable SSID broadcast, the problem goes away and everything is fine.  I talked to someone at Linksys and they are looking into the problem and will be doing testing, but I am starting to suspect the problem is due to the TrueMobile 1300 card and the drivers/utility with it.  Using the Windows XP Wireless Zero Configuration Utility, I am having the above problems.  When I turn off zero configuration and try to configure manually, WPA is NOT available in the Dell Wireless Configuration Utililty - only WEP is available.  This is leading me to believe the problem is in the Dell drivers/software. 

Could you test to see if your problem is the same (ie disable and re-enable SSID broadcast to see if there is an affect). 

Has anyone else had a similar experience?

P.S.  I am using the Windows XP WPA patch and the newest versions of all drivers, utilities and firmwares.

I thought I had WPA support because I download almost all the updates from windowsupdate.com, but I did a search for WPA on the microsoft website, found the fix number (Q815485) and then cross-referenced it in the add/remove programs and determined that I did not yet have it installed.  I am going to restart now and see if my problems are taken care of.

btw, the url to download the update is:  http://www.microsoft.com/downloads/details.aspx?FamilyID=009d8425-ce2b-47a4-abec-274845dc9e91&displaylang=en

Then perhaps the problem is the firmware for the router afterall.

I have found that if I first try to establish the connection with the SSID broadcast turned off, I have nothing but problems, but if I turn it on, set everything up, and then turn it off, everything is fine from there on out.  But for some reason, if I set it up for WPA and SSID disabled, I have major problems.

I did not realize that linksys sold any of the 802.11b products that were WPA enabled out of the box, most companies only sell 802.11g products that are WPA enabled out of the box and for the most part, WPA is only now making it's way into 802.11b products.  Many manufacturers will never support WPA on their 802.11b products.  Check to make sure that you have downloaded the patch for Windows XP to support WPA (that is required no matter what, even if you have drivers that enable WPA support).