Help- 2000 Nissan Sentra GXE problem

[tws_D]

I have a 2000 Nissan Sentra GXE, which has a new battery since January 2012. It's been working well. In the past 7 months (Dec 2012- June 2013) when I needed to use the car at 5AM almost every day, it could start well even at 10F degree, except one time that I had to wait for 5 min. What happened was when I turned the key to the position before I started the car, all lights were on except the engine light and O/D off lights. I couldn't start the car. So I waited for 5 min and then I heard sound like "zizi", like an electrical sound, then both lights for engine and O/D came back on and then I managed to start the car. I waited because it happened before. Every time I can't start the car, it was when lights for engine and O/D drive light were off. It usually works after a couple minutes after I wait. And It usually happens on a humid day. That's why my friends think it may be an electrical problem.

Since early July 2013, I used my car less frequently. What happened recently is I didn't use my car for 5 days of vacation, then I used it for 15 min highway drive and the next day 5 min local drive and left it in a parking lot for another 5 days, during when it rained everyday. After I came back, the car didn't start. Again, only engine light and O/D off lights were off when the key was at the position before starting the car. I had a truck to jump start my car for 10 min, but it didn't start the car, which is not surprising. I waited for almost 30 min, and tried to start my car. It started. I was gonna get out and wanted to shut the front hood, before I even reached the hood, the car died in a sudden.. That was the first time the car died during the time it was working. After 3 sunny days, I came back and was able to start my car.. So I drove it back to the parking lot of my apartment, which is 5 min away. On the way in a plaza, it died again when I was on 5 mph. Then I restarted it and was able to drive to the destination.

I tried to start the car the next day. It started. But then the O/D drive light is on and off and the car is a little shaky. It feels the car is dying anytime. I don't think I'm able to drive it before the problem is taken care of.

Anyone has any idea what is wrong with my car?