It's not the droid, it's your laptop. It's not possible for the droid to prevent another device from working. Almost certainly an IP conflict.
The droid is given an IP by the router, then when you turn on the computer it attempts to use the same IP. Since the droid is already connected using that IP, the laptop has no connectivity.
On the laptop, open the network configuration and make sure it's set to obtain IP address automatically. In windows XP go to control panel, network connections, wireless network connection (or whatever your wireless connections is named, sometimes named whatever your wireless card is), properties, Internet Protocol (TCP/IP), properties, obtain ip address automatically.
I don't use Vista or 7 but the setting should be in a similar place.
I'm 99.9% sure that's the solution.