My model is almost the same as your model ...
Model ES7037CMB - Over the past month the Panasonic shaver would turn on with 3-4 tries, but now will not turn on at all – the on-off switch must be bad after only 7 months of wet use.
Before sending in I found this diagram:
Remove bottom Phillips screw & end cap, pop off each plastic side with fingernails (reinstall them from top 1st), remove 4 screws, remove 2 clips, take top off.
Remove battery case and the on-off little, white plastic lever fell out.
Slide off the white plastic/metal on-off slider & clean contacts with knife … my bottom contact was black & top was clean.
Reinstall on-off slider (white plastic with metal contacts) by sliding back in grooves -- hardest part - place the on-off plastic lever on the battery back unit – I tried to put it on the case and could not get it to stay on.
Slide the battery pack back in with the plug prongs in the holes in the end being careful not to drop the on-off lever.
Stuff battery wires inside case – screw 4 screws and add 2 clips on, then final screw in the end after cap placed on.
Easy once I knew how to put the on-off lever on the battery side – that was tricky.
Total time was about 1 hour – next time it will be about 15 minutes.
Works great! jgg 12-27-08.
Think I will use it dry from now own since it had a lot of whiskers inside of it and maybe wash only the head as needed with baby shampoo.