You multi-meter probably has a continuity test. It will show open vs "short" or something like that. Basically it runs a small current through the leads so you can test end-to-end. Touch the leads together and it beeps or something. Assuming you have this, it will tell you:
Center pin of atty -> button-atty-side
button-atty-side -> button-non-atty-side (when pushed) **** check this 1st **** if fail you fried/melted the button
button-non-atty-side -> battery connector and/or switch
battery-ground->atty-shell
mater switch conacts
etc.
You do all of that with the batteries removed.
Look for hollow solder joints this way.
You can also test voltage with batteries in, but know what you are shorting to what.
Heat sink clip:
http://www.radioshack.com/search/index.jsp?kwCatId=&kw=heat sink clip&origkw=heat sink clip&sr=1
Although you can use an alligator clip, the heat sink clip is flat and has more surface area to contact a flat lead. It fits on the contacts for the button I was discussing.