Off the shelf digital multimeter available at wally world. set to ohms the little omega symbol in the lowest possible setting, and measure from a solder pad to anywhere metal on the heat sink to see if you have a short.
What might help you determine where you have issues with your solder is a continuity test. There is a diode/continuity test on most even cheap multi meters. It looks like a diode symbol, or if you aren't familiar, it is a little line with a triangle pointing at the flat side of the line. If you put the meter in this setting, you can in theory power up each LED by putting the red lead on the meter on the + side of LED and the black lead on the -. DO IT WITH THE REST OF THE POWER UNPLUGGED. In theory, if you do this touching your solder joints, you can find the bad ones.
If my instructions suck, try googling how to use a multimeter to check continuity, someone out there has to have a youtube video or an ehow posting.