Detailed root cause:
Layer 2 security key exchange did not generate multicast keys before timeout
After a long research, I thought that I found a way to fix that. I went to Dell drivers site and wrote my laptop Service tag to get appropriate driver updates. I downloaded the one for my wireless adapter: R198377.exe. The reason why the research was long is that I had to do it on another OS and wanted to find a sound solution not to fail and return back. The dates for the driver were earlier than the date I purchased my laptop but it seems like the drivers coming with it are pretty old.
After installing that, my wireless card -surprisingly- immediately connected to the wireless network. I was gonna say "Well done!" but it turned out to be a coincidence that it worked! After a restart, it was the same problem again. Re-installing driver didn't work. Sigh.
I don't know what to do with this.