Can you tell us which model of Dell system you're using, the type of wireless card you have in that system, the version of the wireless driver that you're using, as well as the brand / model of wireless router you're connecting to? Are all the laptops running the same version of Windows, using the same wireless cards and have the same drivers installed? And what about security software? Is it all the same?
I wouldn't necessarily rule out updating the firmware on the router. Different cards, drivers, and versions of Windows have different connectivity requirements and updating the router's firmware may resolve the issue.
I would recommend that you first check out Dell's Networking & Wireless Support Center. There are quite a few troubleshooting and informational articles there that may help you out.
Please give us a bit more detail on your system, the network you're connecting to, and what errors (if any) you're seeing when you connect, and we'll see if we can find more detailed suggestions to give to you to help with your connection issues.