Hi mate, firstly, the engine doesn't have to run to do a compression test, but in your case you do need to know what part of your engine is leaking. Could be rings and bore, spark plug, the head/base gasket gone or crankcase seals/gaskets. As an engine is basically a pump,(sucking & blowing) do the compression test again and if you can't hear the leak then brush soapy water around these areas, this should show up the leaks, therefore telling you what remedial work needs doing. If its rings/bore then yes a kit would be one easy fix, the other is a rebore + new piston & rings. good luck.
Chris P.Duck, January 2011
