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On older units it could be a number of things:
Thermal cut-off
Hi-limit thermostat
Cycling thermostat
Timer contacts
Motors heater centrifugal switch
Heating element which you have already replaced. Note that it is not unheard of to receive a bad replacement part.

But first I would check the power.
The motor and drum light work off of half the line (120 volts) but the heater requires both sides of the line (240 volts).

Try flipping the breaker off/on slowly, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be careful as 240 volts is lethal !!! [/COLOR]