I unscrewed the top cover and cannot see the end of the cable to remove it. I would like to get some help before I start taking the shifters apart too much. Thanks

There should be a black cap that screws off on the bar end side of the shifter. Take it off and then push the wire from the stem side toward the opening you just created. The head of the shifter cable should come out of that hole. Once the head is out, just grab it and pull the rest of the way out. Feed new cable through that hole when reinstalling. Sometimes, you have you shift gears a couple times to get the holes to line up to make it the easiest to get out and back in. Hope this helps.

Useful tips here:
https://www.parktool.com/repair/readhowto.asp?id=117

I asked the very same question about two weeks ago in the mechanics forum the link here will take you the answers you seek.

https://www.bikeforums.net/bicycle-mechanics/371962-06-deore-shifters-cable-change.html