I don't know if Jazz head gaskets are a problem generally...certainly the 5 I've had have never been a problem.
Having said that the symptoms you describe could be head gasket leak, coolant enters the cylinder then the engine 'hydraulics', cannot turn over to due water in the cylinder. If getting the spark plugs out was simple then this would be an easy way to test if it then turned over and the water could escape out the plug hole.
There are test kits available that will check if combustion gases are entering the coolant...draw a sample of coolant mixed with a test liquid which changes colour if gases present...sure sign of head gasket failure.