A bad ground wont drain your battery, but it will prevent it from charging fully. Although if it goes dead over night, you likely have a key-off power drain, or your battery is just no good.
You can run the car for a bit, to make sure the battery is fairly well charged, then shut it off. Try to restart it, if it starts you should be sufficiently charged for the next check. Shut the car off and disconnect the battery, leaving it overnight. Hook the battery back up the next day and it should start right up. If the battery is dead after it being disconnected overnight, clearly the battery itself is no good. If it isnt dead, then likely you have something consuming power with the key off. Often overlooked things are:
-glove box light that doesnt shut off, trunk light, underhood light...etc
If you have a way of measuring the current draw from your battery with the key off, you should find somewhere around 25-60mA to be normal accounting for clock, stereo memory, pcm memory, and keyless entry module standby etc.... anything over 100-125mA is a cause for concern. 300mA + will definitely kill a marginal battery overnight.
If your current draw is huge (over 3A), look for things like power lock switch stuck, power seat switches, shorted regulator in the alternator etc...