Well firefox has the feature that I think you're looking for (if I understood you). If I have firefox windows open, and I shut down my computer (without closing those ff windows) then when I next turn on my computer and double click ff again, a window pops up asking me whether i want to restore session or start new session. If I click "restore", then firefox will bring up all the same windows & tabs that I had open before and take me back to those very same websites in each window/tab, so that everything is the same as before I shut down.

But I don't know if internet explorer has such a feature; I was under the impression that only firefox has this, but I'm not sure.