Laptop shutsdown when doing e-mail

This has to do with the communication to your wireless router. You can setup your protection on your wireless router to WEP type with a login password and it should eliminate the problem. However some users have interference from software (ei: Fusion),
Also, try resetting your network in this order:
Turn off all comps, routers, modem.
Then first turn on the wifi router and let it boot. Be sure everything else is off.
Then secondly, with the e-net cable connected just between the router and the modem, turn the modem on and it will recognize your wifi as the "computer" address and then turn on all other peripherals and comps. This will allow your wifi to get control of delegating all mac addresses to all other parts of your network and you should have less issues.
Be sure to put WEP password on it too, to keep freeloaders from grabbing your network.