First off you need to do some fault finding with more detail, I.E what is the power at the battery with the car running?, The fact the battery light is not on when running suggests the charging system to be ok.

After the cars been running I guess by the way your talking it can't be restarted without charge? If so if left for a night or so is this then when it won't start again, after charge? The latter indicating a drain.

If you don't have the tools, or know electronics the cars self diag which can be accessed through the dash LCD can be used to check voltage, let me know if you want to know how to do this.

Martin