The display panel light on our double oven has gone out. The clock started to dim and gradually went completely out. The controls and oven work fine, but we aren’t able to check that we have set the correct temperature or time.
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=JJW8630CAB
This is usually the control board, Item 3 Section 2.
Looks like it is out of stock may even be obsolete, you will have to call/email AppliancePartsPros for a delivery date.
The most common cause for this is that an electrolytic capacitor on the board starts to leak current so cannot hold a full charge and the display dims till the capacitor starts leaking so much current that it shuts off.
I do not know which capacitor it is but they are relatively cheap so if you or someone you know has some electronics experience replacing them should fix the problem.
Here is a link to a thread about this problem
http://forum.appliancepartspros.com/oven-repair-including-ranges-cooktops/1058-thermador-display-very-dim.html?highlight=display