I'm sure someone on here will know what's wrong


ford focus 2004 diesal 1.8 tdci

battery light comes on after 30 seconds. been driving it for weeks with this fault. obviously front windscreen demister is disabled because of this.

a few days back I started car in morning. switched on back demister electric. dropped little one to school. got back in car and car failed to start. not enough juice.

jumpy started it and drove but electrical power kept cutting off. needles going haywire etc.

got it at home now. plugged into mains and left it to chsrge the battery via an extension lead out of the window. seems to be starting fine now.

not sure what the fault is. some say battery others say alternator. with some saying smart charge harness.

any ideas or what I should be testing. don't want to fork out 100 quid for a battery if that isn't at fault.

any ideas guys?