Two weeks of sitting is certainly not enough to kill a battery, unless something is draining it, or unless something is simply wrong with the battery..
What is the resting voltage of the battery.. It should be about 12.4 volts or so at 70*F..A little less if it's colder..
You need to check for a bad connection at the battery..
If something did discharge the battery, 5 minutes would probably not be enough to re-charge it, which, BTW is very hard on your alternator..
Probably the best thing to do is take it out and have it properly tested..
If the alternator is not functioning properly, the light would likely be on.. That system works pretty well...
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