A broken trace means that one or possibly more of the circuit traces (or paths) that are within the board are stretched to the point where they break. This creates an "open" which effectively stops that portion of the circuit from working.
To rule out a short to the case, you could remove the motherboard and enough hardware (HDD, RAM, video card) to start the machine and hook everything up outside the case. If you are able to start the machine outside the case you'll know you're looking for a spot where the motherboard is shorting or touching the metal of the case. If it won't start, I'd almost bet that there is a bad circuit in the board.
Video circuits load through the RAM and so do HIDs (Human Input Devices) such as the keyboard and mouse. A broken trace in this area can sure cause your problems.
Edited by wannabe1, 08 December 2005 - 07:46 PM.