I just replaced the battery and it goes dead after about 8 days. How can I find what is running it dead? Seems to be more frequent when its cold.

try your alternator

Make sure all your battery connections are clean and tight. Have alternator tested. It should be putting out 14.5 volts or so.

www.youtube.com/watch?v=KF1gijj03_0 -- check this out it might help if its not battery or alternator issues

every 2003 and 2004 saturn ion 1,2,or 3 has a recall on the ignition switch after 60,000 miles don't waste your money on batteries or alternators. Go buy a 30 ignition switch and watch a youtube video on how to fix! Save you a ton of money. Trust me i have a 2004 Ion that i thought was a bunch of different things untill i called the chevy dealer.