NETGEAR ReadyNAS RND4000 v3 not appearing on network

If the NAS is coming up as 192.168.168.168, then that is the default and you have not set the NAS to have a fixed IP address.  OS re-install is not needed.  Does it also show that address when you connect it to the router?  It shouldn't.  If it does, then your router is not set up properly to be a DHCP server or the ethernet connection to the NAS has an issue.  Do you see activity lights blinking on the NAS ethernet port?

Your public IP address is immaterial, or at least should be.  Your computer needs to talk to the NAS via your intranet, not the internet (except via ReadyNAS Remote, but let's wait for that).

Assuming you are using Windows, open a command prompt and type IPCONFIG.  It should tell you what your computer IP address is and what the router's (default gateway's) addresses are.  If the first 3 numbers of the computer's address and the NAS's aren't the same (meaning they are not on the same subnet), then that's your problem -- we just need to figure out how you got there.

If they are on the same subnet, then open a File Explorer window and type the NAS's IP address preceeded by two backslashes in the address line at the top (like \\192.168.0.10).  If your logon name and password are different from the account on the NAS, you should be asked for a name and password (remember they are case sensitive).  And once you have entered them, you should be able to see the shares on the NAS.

If that doesn't work, you can go back to directly connecting to the NAS and somebody can help you set a fixed IP address on the computer (or just Google "assign static IP address").  But please state what OS you are running so you get the right instructions if you want more help here.