If the battery is a problem the BIOS should show a message on boot, to the effect that the setup is lost and press F1 to continue.
Where it might be a problem (and resetting the BIOS replicates this, or vices versa depending on viewpoint) is with your boot device. AIR, Windows pre-8 didn't understand BIOS notification of SATA drives. There is a hotfix to sort that out, but another common way to deal with it was to tell the BIOS to report SATA drives as IDE, thus fooling Windows into thinking it knows about the drive. The effect of getting this wrong (that is, having the BIOS say 'SATA' when the hotfix hasn't been applied) is a failed boot, which could be the dash you're seeing in the top left of the screen.
So, knowing that, a failed battery or BIOS reset could result in the BIOS defaulting to report SATA drives as SATA drives, causing a Windows boot failure.
From your symptoms, I'd hazard a guess that your Windows version is 7 or earlier and that the BIOS battery is OK. Your network problems might be down to the cable connector.