Computer shuts down except in safe mode

about two weeks ago my computer started shutting down every hour or so after my son began using the modem to hook his xbox to the internet. The computer would be unhooked from the modem and the xbox hooked up then when I needed the internet we'd unhook the xbox and reconnect the computer and reboot the modem so I could connect. At first it was about an hour before it would shut down but the time got shorter and shorter. Now I can only start the computer in safe mode. When I try a normal start up it shuts down before I can put the password in to log on to windows. The modem is a motorola SB5101 cable modem. The computer operating system is XP Home version 2002 service pack 3. Already cleaned all the dust from inside the case, fans are running, went through the event logs, and corrected the time and date to current. It runs fine in safe mode and safe mode with internet. But when I try a normal start it still shuts down.
 
a re install isn't possible. the computer was purchased with win xp installed so no disk. It still runs in safe mode but csnt get past the welcome screen in normal start-up. This started when my son started hooking up his xbox to the modem to play online games. Every time I disconnect his xbox and reconnect the ethernet cable for the computer and try to go online (in safe mode) I have to restart the modem and computer several times. I looked at the event log but don't know what it is I'm supposed to be looking for. Does anyone know if there is something in particular I should be looking for?
 
This is a last ditch effort short of a Clean install... Download Combofix and copy it to the desktop in Safe Mode with networking. Run Combofix, let it update and install a recovery console if asked. Let it finish and don't do anything with the computer until it finishes. Try booting normally... If this doesn't work, you will have no choice but to re-install Windows fresh
 
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