Hawk: I'm having a little difficulty understanding your setup. What Make/Model specifically is your home wifi router?
So, your desktop has the failing wifi card or is it the laptop with Win Vista Business x32?
To try and check for some general things in the router setup: #1) Ensure that you BLOCK ANONYMOUSE INTERNET REQUESTS; and #2) Ensure that your Desktop with Win7 Pro x64 still has a STATIC IP ADDRESS!
It sounds like your were using ICS *Internet Connection Sharing*, which is peer-to-peer sharing and often you may have inadvertently changed the STATIC IP ADDRESS in your Destkop adapter to something different in order to get your bandaid ICS internet connection working through the Vista laptop. I've done this myself. Go back and double-check you still have a Static IP in the desktop adapter settings, and that it's the correct one for your subnet. Probably the one you were using on the Desktop prior to your wifi adapter failing; if you have that documented somewhere.
Without #1 and #2 above, your RDC connection will not work!
I'm not sure about which laptop had the IP address reset, but you may have difficulty running a static IP address on the Vista Business laptop at your office if they have a firewall with Radius Server or a Proxy Server. You may only be able to run a Dynamic IP address on that laptop on your office network, unless the IT Director gives you a special port to "punch" through to run Static-to-Static IP RDC. Most companies won't allow that, as it's a big hole in the firewall so to speak. If you are stuck running the Dynamic IP on your Vista laptop at the office, you should still be able to get through their network and do RDC. Unless they have some specific devices or rules that prohibit that traffic. Again, you'll need to speak with your IT people. Often, they will not allow that type of traffic, and may require you to put a VPN router in your home in order to make that sort of connection. Some companies will supply and install for you, others like the Law Firm I worked for made you purchase the equipment and pay to have it installed.
So the answer to your first question, is "Yes". The 2nd question, about the port # in the laptop; I think you mean the IP address in the laptop, and the Port # in your wifi router. And "No" you don't want to change the Port from #3389, otherwise your RDC won't work at all!
The 3rd question answer is, "Gee, I dunno!"; since I am having trouble figuring out your setup, I can't tell whether RDC will work or not.
But, you should try replacing the wifi adapter in your desktop with a hardline ethernet cable from the desktop NIC to the wifi router to test. This will tell you if it works, that your wifi adapter in your desktop is faulty and has to go. (is the desktop wifi adapter bus-based or usb?).
I answer all 3 of your questions here as best I could. More information would be helpful, but you have the basics on what you need to do.
Lastly, I would try to get the Win7 desktop doing RDC with your Vista laptop in your home environment first, and then take the Vista laptop into work and try to figure out how to get it to work through your corporate office network--that's gonna be real difficult even with your IT department helping you. However, if you can tell them that you have RDC working in your home on the same subnet between your 2 computers, they will be able to help your work through the problem with much fewer headaches. Don't be surprised if they won't let you do RDC from your office at all and suggest a VPN connection or something like GoToMyPC. And in today's economy, don't be surprised if they ask you to pay for it as well!
Get back to us on your specs and answers to my questions when you can.
Let us know if you solve before we close the loop!
Best of Luck,
BIGBEARJEDI