uglybastard
Autocross Champion
Moving the ground won't cause any draw that wasn't' already there. Also, 10 minutes isn't long enough to let the alternator charge a battery that needed a jump. How old is your battery? Car batteries do not recover once the voltage drops too low, if you've had to jump it twice in a couple of days, then you need to have it tested, there's a very good chance that no matter how far you drive, the damage has been done.
pretty much the answer i expected. my mechanic also noted a long while ago that my alternator was knocking a bit or something. maybe that finally went too?