Quoted from statictrance:I found that if you put leads on the two power pins (5v and ground) I show continuity, which I believe is seriously incorrect.
I am only speaking from my experience (please do not take as gospel). I've had to deal with this TWICE now and just today I went to a friend's place to test his repair of a System 11 MPU and got no boot. Several boards (and no boot) later I finally discovered that I had a +5V to GND short (exactly like you I set the DMM to continuity and put one lead on +5V and the other on GND and got a buzz). I didn't blow a fuse because I was using a switching power supply that was detecting the short and not frying itself. So now this will be the THIRD time I've had to deal with this. For me the short was isolated to the low voltage Rottendog display I was using and didn't damage the MPUs I had connected.
The only way I know how to deal with this (I'm open to any suggestions) is to literally take off anything connected to +5V and GND to isolate the faulty component. I de-solder components one by one until the short disappears and that's the component causing it. It can be anything from a capacitor to an IC. One of my friends suggested cutting the VCC leg of each IC until you find the short and then soldering the cut leg back onto the IC. This prevents removing too many ICs but it will look really odd once the board is working again.
Your board looks to be surface mount so it's even more fun. 
