Hi Gerry, I've got the back of our TCE501X as one of the switches has packed in. It looks like a very simple job to replace one of the hotplates.
Switch of the mains supply to the hob (I'd be tempted to flick the trip-switch off)
Pull the whole hob out of the worksurface and you'll see a small panel where the mains cable goes in, this is secured by two special screws, if you don't have the right tool I was able to use a pair of pliers to undo them.
Once this is open, you can unscrew the mains cable and pull it out of the way.
Take the whole hob and put it hotplate side down on a flat surface. You will see two 10mm nuts in recesses, unscrew these and then the back cover will just pull off.
Carefully remove the four wires from the hotplate you're replacing, making a note of where they go.
Then undo the 10mm nut securing the hotplate. Two of the hotplates have earth cables so you may have two 10mm nuts to undo. The hotplate should then just pull/fall out easily.
Then like they say in the Haynes manuals, refitting is the reverse of removal, ensuring that all the cables go back in the right place. If it still doesn't work, suspect the switch which seem quite susceptible to water ingress.
Hope that helps, I can email you a picture with the back cover off so you can see how simple it all is.
Ken Adolphe, August 2009