Hello again. I come back for more wisdom

So, a computer we own with Windows ME is being stupid when it comes to shutdown. About 75% of the time, when we select SHUT DOWN, it actually restarts. 25% of the time it successfully shuts down.
We recently got DSL (modem model GT701), along with a router (LinkSys Etherfast Cable/DSL Router with 4-Port Switch), so perhaps this is a network issue?