Most garages should have a battery tester (instead of a simple voltmeter) to test for weak/dead cells. What make is the battery? Perhaps you just need to top it up with distilled water? If it's still in warranty you can try to claim it.
EDIT - actually 12.4v sounds about right...
http://www.buchanan1.net/lead_acid.shtml
http://www.aa1car.com/library/battery_runs_down.htm