Absolutely NOT modem related. You should have posted that in Desktop PCs.
Top possibility:
In the BIOS settings, some Wake on (something) is enabled. When booting, use the Del key to go into the BIOS settings. In some cases, you need to use one of the Fx key.
Find Wake on (something). There should be a few, like Wake on LAN, Wake on WAN, Wake on phone...
Make sure that they are ALL set to Disabled, except, maybe, Wake on keyboard or possibly Wake on mouse if you want to be able to start the computer by touching a key, ANY key on the keyboard or moving or clicking the mouse.
Save and exit the BIOS settings.
If Wake on LAN or Wake on WAN is set, and you are connected to a router or a broad band modem, the computer will almost immediately want to restart as there is always some activity present.
Electro
February 2012