After system restore lost my i net ip thingy?

Hi  Im hoping someone can make sense of this for me, Im not sure of terminology but thanks for reading and assist in advance :)

First edit to my post: my ie8 is still intermittedly only opening in task manager but wont open for me (its running but wont open) Why?

Orig post:

I know syst restores arent always best way to go but found it ness after scanning evy thng' and deciding Id goofed up some settings and had to start fresh.

This was my laptop which connects to my cable modem by way of a cable to my wired router.

After the restore on my win7, all updated,nis 2011 laptop, it wouldnt go online couldnt find connection to the plugged in lan cable to router but the desktop was fine.

On trouble shoot it said it had outdated or expired ip or something (that number that gets assigned from isp daily or whatever to use online).  thats the term I cant give correct name sorry.

How would I of fixed that easily?   I ended up undo'ing restore and fiddling about till it worked again.

But what was the right way to fix it?  At first I thought it was norton because when I turned it off it came on but it was only running on admin side of pc not limited.

It is back I just want to know if i have to keep a restore how to get my i net back?

Thanks for decoding my question.

(initially I did restore thinking that last week when I fiddled w/ what applications were running-not start up- in msconfig  I goofed.   Because ie8 wouldnt open only ran in task manager..I reset ie8 and add ons and I think it came back from that but the system restore initially was from ie8 not opening but running.)