First of all I would like to thank you for your instant reply. Your guidance is more than helpful for my case!
Even though I configured the IPs as suggested, I didn't try the "PPPoE pass through" mode.
I have already updated the RT-N66U to the latest official firmware. I will try later your suggested configuration and I will post the results.
Since you are also familiar familiar with my particular modem (Draytek), I would like to know if you also faced any difficulties when connecting to it through a PC using an Ethernet cable. If yes, I suppose I will have to send the device for checking. The modem usually disconnects on its own, and instead of getting an IP of 192.168.1.x format, I get a completely different IP (i.e. 169.42.x.x). Is this normal?
I have also purchased a 2nd RT-N66U for a friend. This device is supposed to get Internet access from a modem/router (not from just a router). Do you know how should I configure both devices?