Wreless problems when Router turned off/on

Essentially every day, my dad will turn off the wireless router and DSL modem (Unplugs them both), to help save some power. Now, I don't usually remember to check the connection until after I turn on a computer, and realize that I have no connection.

The trouble starts when I turn the router back on: According to AirPort, it will connect to the router fine, but I get no real internet connection. To be able to reconnect, I have to go to network setup/wizard (or whatever the proper name is), make a new location, and connect to that. I can then afterwards switch back to "Home" and it will work fine on either one.

I have never had this sort of a problem with any of my other computers, so I was wondering if anyone here could shed some light on some sort of a solution.

PS: The problem seems to persist even after restarting the Mac, if this helps any.

I would first suggest to just keep the router and modem on. Secondly, my guess would be that you are having problems with the router/modem because of the turning on and off. I've noticed a lot of times (especially with DSL using PPoE) that users experience problems with there router acting as a DHCP server when they power off and then power back on. You may need to go in to the DSL modem configuration and make sure the configurations are set up correctly--such as PPoE with the correct account name and password.

But I think life would be easier if you just left the modem and router on.

I second that.
Those devices don't consume that much power, and turning them off isn't going to show any significant savings. Turning them off will interrupt the DHCP as was mentioned, which is the cause of your problems.