First of all, some background. I'm using Vista Ultimate x64 on PC1, XP SP3 32bit on PC2. Both are connected by Ethernet cables to a Speedtouch 706WL, which in turn is connected to my ADSL2+ line.

The Speedtouch was acting very funny, so as a last resort before getting a new modem, I tried flashing the firmware ro see if that'd help. It didn't, but that's not why I'm here.

Ever since I tried flashing my firmware, one of my PCs (the Vista one) is no longer getting recognized by my modem/router, meaning it doesn't show up in the Devices list no matter which port or which cable I use. My second PC, however, works fine on both ports.
So I checked ipconfig on the PC that was giving me problems, and I noticed the Realtek network card that's usually in that list was no longer present. I checked the device manager, and the card is still there and working properly (it shows up as Realtek RTL8168B/8111B Gigabit Ethernet NIC (NDIS 6.0), and it's actually an on-board card on my Gigabyte GA-P35-DS3R). I tried re-downloading and re-installing the drivers, but that didn't help.

Could anyone tell me how I can get my Ethernet connection back?

so your nic was present and visible via device manager before you flashed the firmware? if so and its not working now then, the flash may have cause it or it flashed the firmware and vista is acting up. I'd suggest reverting back and see if that restores it. perform a system restore if needed.

your NIC should at least show up in the device manage, even if the drivers arent loaded or loaded incorrectly, it would just have a yellow exclamation point or red X on it.

I'd suggest a system restore a day prior to the day you did the installs and see if you get it back