Punto starting problem

Punto 1.1 petrol (M plate)
My wife's car was acting really strange yesterday. Temperature setting was jumping about all over the place. Would go away up to the red and then back
to normal in a matter of a few seconds. Even when it came to rest the needle would be shaking away. While this was happening the "injector light" would occasionally come on and off. Anyway we stopped the car (didn't switch off) had a quick look under the bonnet but noticed nothing untoward.
Got a mile down the road to where we were going. Switched off the car. When we got back in and tried to start it, it was dead. No engine turn over at all. The battery is fine. Strange thing is when you turn the keys to the ignition (without trying to start it) you can hear a clicking on and off like a "relay" gone mad. This results in the ignition lights blinking on and off in sync with the "relay" noise.
I've tracked the noise down to a wee box in the engine compartment located at the back of the engine covered by a large hood. It is alongside two fuses that seem unconnected with it. There is nothing in the Haynes regarding this.
Anyone know what this unit is likely to be? I thought at first it was something to do with her built in immobiliser as she has had to use her red key a few times to get the car started but that is now ruled out.
Thanx for any info
Steven.
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Bad earth or the battery has had it.
Try putting an earth from the engine to battery neg with a jump lead.
Measure the battery voltage on crank. Check all earth points.
A buzzing relay is caused by insufficient voltage, so you are back to battery voltage or poor connections.

How do you know this?
Garry
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I'll try these suggestions. When I say battery is fine, I mean it has enough power to work lights etc, and should have enough power to at least attempt to turn the starter motor. But there as absolutely no response when trying. Also the battery was replaced about 2 months ago so should be okay.
cheers
Steven.
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motor.
You were right Garry. Turns out the earth strap from the gearbox to the side of the engine compartment had sheered off.
Thanks for your help.
Steven
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