The Silvia is a really simple machine. My first suspicion would be that it did not get rewired correctly when the thermostats were replaced.
I won't speculate how the wiring might be wrongly done, as you can download a schematic and carefully trace where everything should go.
When you switch on a cold Silvia, the power to the heater goes in series through the brew thermostat, then through the steam thermostat to the heater. Because the brew thermostat opens at a lower temperature than the steam thermostat, when the boiler gets to temperature, it opens and power is cut. When you're brewing espresso, nothing changes in the heater path...power just gets applied to a bunch of other stuff, none of which would affect the heater. So, the only possibility here is a shorted brew thermostat.
When you're steaming, all that happens is the steam switch shorts out the brew thermostat. So, this is another place to look. Simply take the wires off the brew switch to eliminate any possibility that the brew switch is shorted.
I can't think of anything else that might cause your problem.