Desktops :: Full Hard Drive On Mac Mini

My son is having a BIG problem with his Mac Mini. His Mini has a 1.83GHz Intel Core 2 Duo processor, memory of 3GB 667 MHz DDR2 SDRAM and runs Mac OS X Version 10.6.3. He has Time Machine and also a 1.5TB desktop hard drive. From time to time, he has been getting pop-up warnings that his internal hard drive was about to become full. He would then do some deleting and things would be fine until the next pop-up. Last week, after watching some videos on Utube, he tried to open iTunes and, instead of a pop-up, got an error message with some numbers (which he didn't write down). It began the usual routine, starting with a white screen with the apple logo in the center and the loading circle spinning right below it. After that, it normally goes to a light blue screen and then loads the desktop, but this time (and ever since) it stopped at the blue screen, empty except for the message "Hard Drive Full, Please Delete Data".

Apparently the screensaver still works, but not much else -- like the Finder. He said that he did get something to appear on the top bar by taking the batteries out of his Apple Bluetooth keyboard, bringing up the "Bluetooth Setup Assistant", but once a wired keyboard is plugged in, everything on the top bar disappears (since the Mac sees a keyboard). He was going to do a "restore" and, in preparation, thought he had done a successful back-up to his external hard drive using the Time Machine feature. However, when he checked the Time Machine under System Preferences it said that the external HD had nearly 1.5 TB unused (only a couple hundred pictures or so on it) and the Time Machine was supposed to put about 70GB on there. So now he is concerned that he didn't/can't do a back-up.