I have an acer laptop that we haven't used for a while due to a cracked screen, resolved this last week by using a monitor instead. I remembered after a short period of time that it keeps coming up with 'internet stopped working' flag up on the screen (mostly on facebook, don't know if that is relevant). Could this be down to a settings thing or poss a fault, we run another laptop off same wireless box and no probs like that.
As the machine has been offline for a long time, before you do anything else, I suggest that you check for updates.
After you've updated everything, if you still have problems with IE, you might want to consider Firefox or Chrome as alternatives.