I've got a 2003 Civic (EX? Sedan) that is struggling in the colder weather. I made the mistake of leaving it out in the near freezing temperatures and didn't start it for over a week. Now trying to start it results in some erratic and sluggish sounds of an engine that seems to be trying to start but failing to sustain movement. I can even hear it start to turn over a bit with a few rough fires of the pistons, but it just can't keep it going. Electrical systems are behaving fine at a glance, though my dash seems to dim much more than usual during the ignition. Battery is roughly 2-3 years old, though a few months ago I drained it with a light on and had to jump. I've also tried starting it with a jump battery pack attached with no discernable difference.
Is it a lost cause, or is there something I can check/try? My research on YouTube for similar sounding issues hasn't come up with a match yet.