Router Question

Hello,

Hope this is the correct forum for this.
Have never really understood routers, and would like to try and understand this:

About a month ago, I purchased a new Linksys Router.
One of their better ones; two frequencies, N rated, etc.

Installation went fine, and if I remember right, there was a big Security Code number one had to enter that came with unit.
Don't remember if I "also" had to provide an additional password (I can try to look once I figure out how to)

I just recently had to replace the HD in my PC.

Used the set of 3 HP Restore Disks that I was smart enough to create when I first bought the PC about 3 years ago.

Big surprise: the Router connected and worked !
As the router is new, and the restore disks old, can't understand how it "automatically" connected again using all the old restore disk software.

So, where's the security, even after entering the long security code they provided ?
Is there another Password that I could have, but maybe didn't, during the initial router installation ?

The PC is hooked to the router as hard-wired via an ethernet cable.
No wifi for pc
Just use wifi for connecting to iPad.

Is this ethernet connection perhaps merely a "pass-thru" and really doesn't require any of the router's passwords, etc. ?

Thanks,
Bob