EWS problem

[E-series ftw]

I'm guessing by the age of your vehicle that you have a diamond key.
There is a long slender coil on the circuit board that energizes the 6-pin EWS transponder chip (also on the circuit board) when the key is switched to the crank position. The coil gets its power from the transponder/charging ring on the ignition switch. The battery on the circuit board is only required for the remote lock/trunk functions.

If the circuit or components of the transponder circuit on the board are compromised, your car will not crank. The coil is easily cut if you get too agressive with a knife blade, while trying to open the key to replace a battery. Ask me how I know. Water/moisture ingress could also be a cause of failure.