My ho sat for all of December in the garage w/o ever being started... started her up in January and she started fine. And she still has the orginal 6 year old battery in her...
It should start fine if it sits for only a week... Sounds like something more than a battery issue.
Have you looked at the battery? Corrosion can sometimes happen on a battery if it sits too long. Maybe check the battery connectors/ports too... Just start fiddling with stuff, that almost always seems to work for me.