Car only starts when it feels like it

[94_AcCoRd_EX]

Alright, my car is a little messed up and doesn't like to start. I just had the battery changed, and the charging system checked; everything is fine. This problem seems to happen more on cold/wet days. All last week when the weather was nice, I didn't have a problem with it, but its been happening on and off for a month or two.

When I turn the key, there is a clicking noise under the hood, like the starter motor wants to crank, and my interior lights dim (like they usually do when you start a car, just momentarily). Then nothing happens. If I keep the key turned, I can hear a distinct buzzing noise under the hood. Today, I did this about 15 times in a row, and then it just started perfectly. Also, it occasionally will crank very weak but not start.

I'm going to take it by Honda tomorrow (if it starts), but I'd really like some opinions on what to look for.

Thanks guys and girls