How to force Windows 7 to ask for a "fresh" IP address from DHCP server?

There is no procedure worth the effort. It's stored in a registry key, but that portion of the registry is cached while the network subsystem is running. So you'd have to shut the system down, boot another OS installation, mount the registry, delete the key, and then reboot into the original OS installation. The key is DhcpIPAddress but it is only used across reboots, so you can't modify it.

Uninstalling and re-installing the network adapter might work.

Running net stop dhcp and then net start dhcp appears to work on my Windows 7 test system. The resulting DHCP discover packet does not include Option 50.

I guess it's your choice if you want run ipconfig /release first in order to signal to the DHCP server that the IP address is available (it should remove the existing lease on the DHCP server).

So, to summarize, the whole process would be (in an Administrator cmd window):

ipconfig /release
net stop dhcp
net start dhcp
ipconfig /renew

If you wanted to indicate only a connection matching Local* (for example, Local Area Connection), then you could do:

ipconfig /release Local*
net stop dhcp
net start dhcp
ipconfig /renew Local*

This will work:

If your Ethernet driver supports it, you could change the MAC address on the NIC. It's usually a relatively painless procedure. Then ipconfig /renew should give you a new IP address.

I found this solution here.

1. Reset WinSock and TCP/IP Stack
   a. Open a Command Prompt as administrator
   b. Reset WINSOCK entries: netsh winsock reset catalog
   c. Reset TCP/IP stack: netsh int ip reset reset.log
   d. Reboot the machine (you can run both commands first, I tend to put multiple commands in notepad and then copy and paste into the command window).

2. Renew your IP
   Configure your IP settings, whether static or dynamic, and we’re done