Car wont start even with good battery. And check engine light does not come on.

If the battery is fully charged and the starter won't engage this could be a few things. A fault with the ignition switch, the starter, a relay or fuse, wiring. There are many possibilities here and you will need a complete diagnosis. If you have the tools and experiance check the starter for power. If it has power you may simply have a bad starter. Here is a link to find a shop near you. https://repairpal.com/repair-shops Alex