with the computer ON
unplug the modem, wait 15 seconds, now plug the power back in, wait until all the lights are blinking normally...
now repeat the same with the wireless router...wait until it starts up again,
now restart the computer, the network should be recognized. You may need to log in w/ the password.
If the inspiron is getting a weak signal, this would explain the dropped connection.
Replace the router w/ a better one (N speed) (three antennas, or external Hawking antenna)
Walls will block the signal...a weak signal less than 5 bars will cause all kinds of problems. There are high gain external antennas that can help quite a bit.
BUT...wireless internet as a whole is a real pain and has never lived up to it's promises. ALL users of wireless have the same problems. A direct cable connection is 100 times better than wireless.