Auto Electrician here ?

Hi .. I have a EA Fairmont that got a flat battery from a indicator light being stuck on overnight from its alarm.
I charged the battery to start the car and took it for a 15 minute drive too charge it back up ,I left it running in the driveway and it cut out on me.
So I decided to go get the new battery ,I fitted it and everything seemed fine and fully charged. Tried to start ,and wouldnt fire up ,Im getting no problem from the battery,starter, or alternator and only can think its a relay switch.
I am wondering if anybody can advise me how too check a relay switch ,and with what tool will I need to buy to do this.

Cheers in advance

Jono aka jj