Hi JCMTemple,
I understand that re-installing the operating system is a time consuming process and considering you have Windows 7 upgrade from Vista, it might consume more time. I agree with you that all the data on system will be lost during the re-installation, however, as we have already exhausted all the troubleshooting steps, it is recommended to re-install the OS before isolating the issue with the hardware as OS re-installation takes care of all software related problems on system if any.
However, if you do not wish to go that route, you may try installing a good known wireless card in your system and see if that works. For installing wireless card you may refer to service manual shared earlier.
Please reply with the findings. I would be glad to help you.