B9 - key fob/ignition/starting problem?

[Tomcat3]

I had a call out to a toyota with possible original battery a couple of weeks ago the car had started first time every time no problem. It had been driven to work the owner came out a while later battery just about clicked the relay. I put new battery on car fired straight up and been fine since. I tested the old battery when I got back and it had a dead cell.
Eco mode usually displays when the car has shut down to conserve electrics ie when radio left on or low on power.