The computer will not be able to pick up the D-link network I have set up if I switch the modem and router off. Even when I leave it running it will sometimes not get picked up.

Try changing the encryption type. This sounds like the computer your using does not support the encryption type being used by the router.

1. Go to the setup screen of your router. For a D-Link router, you typically fireup your browser, go to http://192.168.1.1, and type in your username and password, my default username and password is admin, admin.
2. Click on the Wireless link. It will open Wireless settings.
3. There are options to let you set your Encryption Preferences. You can provide an encryption key that will be used by the router and any PC that wants to use the network.
4. select none. (if your wifi now works then you have found your problem and you can try the alternate encryption type, either WPA or WEP)