Remove the screws in the mounting brackets that secure the glass cover.

Remove the halogen lamp and the screws securing the metal heat shield below the lamp.

It is unlikely, but the safety switch (red square) may be completely broken and not making contact. If you have a multimeter that can measure conduction, touch the metal contacts that the two wires are going to and press the switch in to see if it makes contact.

If the switch doesn't work, you can remove this from the unit and connect the two wires via a wire nut or solder (and some sort of wire insulator, like heat shrink).

If you have a multimeter capable of testing an AC 120Vrms signal, you can check the voltage across the two Lamp leads (green squares). Be sure to press the safety switch down and cycle through the on settings while testing, but DO NOT touch the leads with your hands, and use only 1 hand if possible to reduce the possibility of a fatal injury if an incident occurs.

If there is no voltage across the two leads then there is a break in the wire somewhere, or perhaps your outlet is dead. Test the outlet with a known working electronic device. Or trace the wire to find the break.