Hi Dadoftim,
Are you really Tim's dad? LOL!
Welcome to Vista Forums!
Before starting, there are three models of the HP Deskjet F2200 series - I need to know the specific model.
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HP Deskjet F2210 All-in-One Printer
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HP Deskjet F2235 All-in-One Printer
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HP Deskjet F2280 All-in-One Printer
Also, what type of printer port are you using on the PC that won't connect (USB Virtual Port, LPT, TCP/IP,...)? Is the printer setup with a static IP address? If so, try setting up a TCP/IP port using the printer's IP address instead of using the normal connection wizard and connecting to the printer being shown and see if that helps (in essence, used the advanced method and be sure to complete everything required).
You may also need to install printer drivers for the printer connected to the x64 machine on the PC that isn't connecting as they may be transferring wireless (so the others work) but not doing so with a direct connection (though I honestly don't know why that would happen and don't think it's the problem, but it's worth a try).
What is the manufacturer, make, and model of the router?
If you can, try connecting one of the 32-bit computers that work with the printer by cable to the router (instead of wirelessly - you will probably need to create a connection for that) and see if it still works or if it now has the same problem. I'm trying to see here if it is a problem with the computer having troubles or with the method of connection. That will help us focus attention in the right area.
I hope this helps. If not, post back with the results of what you tried and answers to my questions and we'll see where to go from there.
Thanks and good luck!