Contrary to what many seem to believe, there is absolutely NO assurance that the IP address of the private side of a router is 192.168.0.1 or 192.168.1.1.
Secondly, there is a major difference between a modem and a router. You call the original unit a modem, later you call it an ADSL modem + router. In checking it out, I see it is an ADSL modem and router. This unit, as is, provides both router and modem functionality. It has only 1 RJ45 LAN port so you need a network switch to connect to more than 1 wired device. It provides no 802.11 wireless functionality. It appears to be using the 192.168.1.0/24 subnet on its private side since you claim 192.168.1.1 entry in web browser takes you to its configuration page. I am assuming it is using the standard 24 bit subnet with mask 255.255.255.0. It links to the phone company feed via an RJ 11 jack.
The NETGEAR N150 Classic Wireless Router WNR612 is not a modem - router. It cannot link directly to the phone company feed via an RJ 11 cable. It has 1 WAN port and 2 LAN ports for wired devices.
You indicate you are having problems but you do not indicate how you configured the unit or how you connected your pc to it for configuration purposes.
I am going to assume that you really want to use the Netgear as a wireless access point and keep the original modem / router to provide modem and router functionality. In this case, turn off and disconnect Netgear from any connection to the modem / router. Turn off your pc. Connect a cat5 or cat6 patch cable from your pc to one of the 2 LAN (not the WAN) ports of Netgear. Connect nothing to the WAN port. Turn on Netgear and at least 2 minutes later turn on your pc. After pc warms up fully open command prompt (start, run, all programs, accessories, command prompt) and type ipconfig at the prompt >) and hit enter. You will be given an ip address, subnet mask (most likely 255.255.255.0) and a default gateway IP address. The default gateway address is the address of the Netgear. Use that address to log into Netgear. Once in the Netgear, disable DHCP entirely and change the router's IP address to 192.168.1.2, mask 255.255.255.0, default gateway 192.168.1.1. Save your configuration entirely and exit.
Power off the modem router, the Netgear, and your pc. Leave pc connected to Netgear LAN port. Connect LAN port of modem router to the other LAN port of Netgear. Turn on modem router; at least 2 min later turn on Netgear, at least 2 min later turn on pc and let pc fully warm up. Now let's check for connection. Open command prompt and enter at the prompt (>) ping 192.168.1.2 and hit enter. You should see 4 successful replies indicating you are able to link to Netgear; next ping 192.168.1.1 and hit enter - again you should see 4 replies indicating you are able to link to modem router. If either ping test fails, you need to review what I wrote to make sure you did it properly.
Next, after both ping tests to 192.168.1.1 and 192.168.1.2 are successful, check for internet connection by using the ping 4.2.2.2 command in command prompt; if successful you are linking to internet. Next check for DNS by using the ping google.com command. If all of these work you have internet connection.
Now all you have to do is configure wireless on Netgear. Log onto Netgear at 192.168.1.2 and configure as the manual directs you to do.