I suspect the DHCP service is actually running for a minute or two when you startup...Windows will automatically assign a "fake" IP address (it starts with 169) to an interface if it doesn't pick up an IP via DHCP...then it shuts down the DHCP service.
Have a look at a few things. First, check to make sure that you're not filtering out the MAC address of that wireless card on your wireless AP. Second, make sure that you've got enough IPs in your DHCP pool to assign another one. You should also (just for the sake of the argument) make sure that the wired NIC isn't plugged into the router...maybe even disable it (temporarily) in the hardware devices panel.
Make sure DHCP is enabled in the card's control panel...and if you still fail to get an address after doing all of this, open up a command line and type (without the quotes) "ipconfig /release", then type "ipconfig /renew". Even if this doesn't give you a new IP, it will often give you an error message that may point you in the right direction.