Mac won't connect to internet

So my macbook os X Version 10.4.11 is suddenly having this issue where it won't connect to the internet. My airport shows I have a full signal but Safari (or Firefox) says I am not connected to the internet and when I click on Network Diagnostics it says:

Airport:Green
Airport Settings: Green
Network Settings: Yellow
ISP: Red
Internet: Red
Server: Red

All the other computers in the house are working just fine.

Here's the odd thing...if I shut my computer down, take the battery out and wait a few minutes, the internet will work...for about 5 minutes.

I've been getting an error message that my startup disk is almost full but I have deleted all of the files I don't use (podcasts, pictures, etc)

Also, Skype has been shutting down after 20 minutes, I repaired disk permissions, that didn't do anything. Obviously it doesn't work at all anymore.

Please help! My girlfriend just moved to Italy and the internet is basically the only way we can communicate.

Follow my posts over in this Thread
http://mac-help.com/showthread.php?t=11767

To see your Available Disk Space do a Get Info on the HardDrive Icon.

Finder > Empty Trash
iPhoto has its own Trash too, iPhoto > Empty Trash. Then check that iPhoto has moved those deleted photos to your Finder Trash, the later version do.

Safari > Empty Cache...