If you replace the battery it will most likely resolve the problem.
Sounds just like what I went through.

On Tue, 04 Nov 2003 02:51:27 GMT, "oct2100" <oct2100@pacbell.net>
wrote:

>I have a 2000 Honda Civic DX (4 door). It only has 40K miles on it but I've
>noticed that the car is very weak to start when I turn the ignition in the
>morning. It starts but normally the starter sounds much stronger when I try
>to start the car. Its almost like it hesitating. I did notice that it
>started doing this once the weather here got very cold and it gets hit with
>occasional rain. I'm almost positive there is a relation. Does anyone know
>if this is a common problem with 2000 model year Civics?
>
>
>