Alienware Area-51 18: hard reset, RTC reset, and network power cycle
Draining residual power, resetting the system clock, restarting the network: three simple moves before assuming a serious fault.

Draining residual power (a "hard reset")
Even switched off with the battery removed, a computer holds onto a residual electrical charge known as "flea power." Clearing it before any repair protects sensitive components, and also resolves certain lockups where the machine won't turn on or won't boot into the system: turn off the computer, unplug the AC adapter, remove the base cover and then the battery, hold the power button for 20 seconds, then put everything back before turning it on again.
Resetting the system clock (RTC)
This clears the BIOS settings and gets you out of situations where the computer won't power on, shows nothing, or won't start at all. With the computer off but connected to power, simply hold the power button for twenty-five seconds: the reset happens when you release the button.
Restarting network equipment
For an internet connection problem, the method is the same as for any home network: turn off the computer, then the modem, then the wireless router, wait thirty seconds, then turn everything back on in reverse order (router, modem, computer). An internet box that combines modem and router in one device follows the same logic.
What order to try these in
For a persistent problem, start with the network power cycle if the symptom is purely about connectivity, then the RTC reset if the computer won't start, and save the residual-power drain for the most stubborn lockups or before opening the machine at all.