Well, I have GREAT news, and it came from a totally unexpected source! As I was forging on with the setting up of Windows 7 on this Inspiron 9300, I found some additional critical updates on MS Update today, but before I installed them I looked at the list of "optional" updates to see what they had to offer. And, right at the top of the list, were a listing for an update for the Intel PRO/Wireless 2200BG adapter, and an update for the Nvidia Go 6800 display adapter (which I also had been unable to update as none of the several drivers I tried from the Dell site or from Nvidia succeeded). So I installed them both, and they were both successful! So even though from Device Mgr. Windows 7 saw only an "unknown wireless controller" in place of the 2200BG, it did in fact know the wireless card is an Intel PRO/Wireless 2200GB and that it needed a driver. And now it is working. How it is that MS Update has this mysterious driver, and Intel does not, I'll leave you to ponder. Ditto for the Nvidia driver. 
Hi folks, I've installed Windows 7 Home Premium 32-bit OS on my Inspiron 9300, and thanks to some previous information found online I have pretty much everything working now except the Intel PRO/Wireless 2200bg card. I have not had any success finding a suitable driver for it. All the ones I try yield that no suitable or pertinent hardware is found, so the driver installation fails.  My AIDA 64 Extreme utility (formerly Everest Ultimate) sees the card and provides information on it, but Windows 7 sees it only as an "unknown network controller" in the Device Manager. I've tried the Intel Update site to no avail, tried installing the recommended driver from the dellwindowsreinstallationguide.com website, carefully following the prerequisite steps before downloading the driver, which also failed to install. The wired LAN card in the notebook works just fine, and I am typing this post from the notebook itself.  The Intel Driver Update website claims to have found nothing when I let it search the notebook, and when I did a manual search for the Intel PRO/Wireless 2200bg card it returned nothing. So I am thinking Intel has likely dropped support for this wireless card. I searched for and found a Windows Vista driver for this card, and after some delay it seemed to install, but then did not open any windows or make the card visible to Win7. Eventually I found this on an Intel Site: "Detailed Description Intel® PRO/Wireless 2200BG Network Connection does not support Microsoft Windows* 7The Intel® PRO/Wireless 2200BG Network Connection is no longer being manufactured by Intel, nor will Intel provide any future software updates to support new operating systems or improve compatibility with third party devices and software products." So it appears Intel has indeed dropped support for this card.  If anyone knows of a way to make this work, I would appreciate any help you can provide. 
Intel PRO/Wireless 2200bg in an Inspiron 9300 - How to get it working with 
Windows 7 Home Premium SP1