Hotplates use a very simplistic technology, so when problems arise the cause can be narrowed to a few simple parts. The power cord, thermostat and heating element are the main electronic elements of the hot plate, and are the most likely cause of problems.
If the power light on the hotplate is not lighting up, the power cord is the most likely cause of the problem and should be replaced. It is important that the voltage of the new cord be appropriate to that of the hotplate.
When the thermostat fails on a hotplate, it will often still heat up, but will not reach an appropriate temperature. These replacement parts may be hard to find, and it may be simpler to replace the hotplate than to attempt repair.
When the heating element of a hotplate fails, it simply stops getting hot. If your hotplate is cool to the touch, disassemble the hotplate and replace the heating element.