Clearly if you charged the battery and it's died after being running a few minutes you need to be looking toward the battery!

How long did you charge it for? You need to see the amount of power it has in it, a fully charged battery will easily be 12.40V +, anything less than this isn't good!

The battery light needs to be working, if not charging won't commence as this is a critial part of the charging circuit, you can get it to charge by revving to around 3K RPM though!

Martin