Alfa battery connections leave a lot to be desired, so I would be suspicious of those, especially since you changed the battery recently. The way to diagnose it is to have the engine running - preferably with all your faults showing, then put a DVM (voltmeter) directly across the battery terminals, read the voltage, then read read the voltage on the battery cables. If the two are different, then your connections are no good.
Aside from that, I can tell you for sure that a duff thermostat on a 156 2.5V6 can make the engine management light come on, as I had that fault on mine when I owned one. But I didn't get the ABS / handbrake lights coming on, which makes me agree more with Sprint's post that it is battery related.