This is for anyone who has had difficulty getting a wireless connection between certain Dell laptops and the good old Westell Versalink 327W router.
The answer is simply that the software for the modem needs updated. The link to get that update, which is version 03.02.01, along with its explanation can be found
here.
This issue apparently pertains to all Dell wireless cards, but is not limited to the Dell brand. Without this update, many residential and small business Verizon DSL subscribers, utilizing this model of wireless router, may have connectivity issues with a range of laptops.
Mysteriously, Verizon's online and phone support historically has not been efficient in diagnosing this specific kind of connection problem, when all along it's been a modem software update issue, created by Verizon to address it.