It sounds like your random disconnect issue is from the modem back, rather than anything to do with your computer.
Who is your provider? Are you on DSL or cable or something else? When it disconnects, what are the lights on the modem saying?
We were using comcast cable here for a while, and we had intermittent connectivity problems. It turned out that the problem was that one of our neighbors had spliced into our line (legally or not, we're not sure), and that basically cut our signal level in half. We called in a tech after a lot of cajoling, and they fixed the issue. Then another neighbor spliced into our line. Repeat.
Then, we had a completely separate problem of really awful lag, which, according to tracerts, was due to some comcast router in the area dropping lots of our packets. Other people in Chicago had this same problem, and Comcast refused to acknowledge that it was their fault, so we switched to RCN, where we get 10mbits down and about a megabit up.