On my Digital Multimeter a figure 1 on the resistance range indicates open circuit - infinite resistance - when the probes are touched together the reading shows close to Zero.
A working 1kw heater on a 230V supply will have a resistance of about 50 ohms 2kw about 26 ohms.
Your heating element appears to be open circuit with a short to earth.
The fuse may blow but the trip beats it to the line.
My guess is that a new element is needed to solve the problem.
Peccavi
October 2010