The IP address range 169.254.0.0 - 188.8.131.52 is reserved for Automatic Private IP Addressing (APIPA); Microsoft PCs will revert to APIPA addresses in the event that a DHCP server or Default Gateway cannot be reached. Windows will only wait 6 seconds for a DHCP leased address to be applied after startup.
Here is the Microsoft KB article which details APIPA:http://support.microsoft.com/kb/255836/en-us
Have you tried to manually configure the TCP/IP Properties and set a Static IP address to determine if that has any effect?
Since there seems to be an issue with one machine receiving a DHCP leased address and ipconfig /release | ipconfig /renew are not helping with the DHCP lease process, try bypassing it altogether by setting the APIPA addressed machine to a manually assigned Static IP address. We know your desktop PC is not encountering any connectivity problems therefore, the information contained in the command output should be viable and allow you to setup a Static IP address on your laptop. Run the following command a the command prompt on your desktop machine:
On your laptop, open up the Network Connections folder, single-click to highlight the network connection which you want to configure the static IP address on (i.e. Local Area Connection OR Wireless Network Connection). Right-click the connection and choose Properties. In the Network Connection Properties dialog box, you want to select Internet Protocol (TCP/IP) in the scrolling menu under "This connection uses the following items." With the Internet Protocol (TCP/IP) option highlighted, click Properties to bring up the Internet Protocol (TCP/IP) Properties applet.
Internet Protocol (TCP/IP) Properties -> General Tab
This applet has two tabs, General and Alternate Configuration. Let's just start working on the General tab, you will want to select the radio button to indicate "Use the following IP address." on the laptop, which you are going to attempt a Static IP address configuration, you will want to copy the following information from the ipconfig output on your desktop PC (or any other PC which is connected to the network with a known functional Network / Internet connection):
Copy this info:
Preferred DNS Server (first one listed in ipconfig)
Alternate DNS Server (second one listed in ipconfig)
Choose an IP address that is close in proximity to your desktop PC - you can just use the next numerical number in sequence, but there is nothing which says you can't use any random IP address as long as it is within the same subnet. I'd advise using sequential IP addresses or moving up in increments of 10. I.e. desktop PC IP 192.168.1.20, setup laptop IP 192.168.1.30. For troubleshooting purposes, keep a standard pattern so that if necessary, you can recall different IP addresses from memory in case the information is not readily at hand.
Once you setup the Static IP address information on the laptop check your network connectivity. Ping the desktop from the laptop and vice versa to confirm that those two machines are able to communicate with each other. Open up your web browser and open up the same web page on both machines. IF this does not successfully achieve a network AND Internet connection on the laptop, switching back to DHCP and APIPA is as simple as clicking the radio button in the Internet Protocol (TCP/IP).
If you find that you are able to successfully connect to the Internet and your SoHo network using the Static IP address, and you would like to utilize this as your primary workaround for DHCP lease problems resulting in an APIPA assigned IP address, you can do the following:
Internet Protocol (TCP/IP) Properties -> Alternate Configuration tab
If you have configured a Static IP address in the General tab and have tested it and confirmed that the numbers are functional, you can set this IP address information into the Alternate Configuration tab for future use, and yet still have DHCP Enabled as the default method of configuring this information. IF a DHCP server is not able to be contacted or a DHCP lease unable to be accepted | granted, your machine will revert to the Static IP address information stored on this tab. Simply plug in the tested numbers you used in the General tab by clicking the User Configured radio button on the Alternate Configuration tab.
There is one additional set of numbers which you will need to record and input on the Alternate Configuration tab which were not options in the General tab, these are the Primary and Secondary WINS servers. This information is listed in the output of the ipconfig /all command.
Try setting a Static IP address and post feedback for more advice.