So I decided to dual-boot my computer with Linux. I've been mildly aware of wireless card problems with Linux before, but I never would have thought that it would be this difficult to get things to work right. Here's the solution, courtesy of a forum post I can't find the link to now. Thanks to that mysterious person user stoat from fedoraforums.org (link to post) who saved me from hours (more) of frustration.

The Dell WLAN 1397 Wireless card is shown to be the Broadcom BCM4312 802.11b/g LP-PHY (rev 01) card through the lspci command. The file needed is called

broadcom-wl-4.150.10.5.tar.bz2

It should be floating around on the internet, available through a quick search. Too bad WordPress won't allow upload of .tar.bz2 files.

Get the file onto Fedora through a USB, then navigate to the containing folder using the terminal. Run the following commands in the terminal

tar xjf broadcom-wl-r.150.10.5.tar.bz2
cd su broadcom-wl-r.150.10.5/driver
su 
b43-fwcutter -w /lib/firmware wl_apsta_mimo.o

Finally, restart the computer. Wireless internet should be working.