New problem

I have a 94 LeSabre Custom. It had a starting problem before, especially in cold weather, but now it has a totally different starting problem. Previously, in cold weather, it would start, but after a second or two it would start coughing and then shut off. However, in warm weather it would start and stay on. Today my wife had to use it for a moment and she told me that it was really hard to get it started, so I went and checked it myself. Instead of the usual symptom, what it does now is like a choke. I got it started just once and it started, but not right away, it took a few seconds, and by the sound of it it was like the battery was dead. I drove a quarter of a mile and came back. After a few minutes I went back to the car and this time there was no way of getting it started. It would do a cranking noise, but very slow, and also the electric system was reset because the car stereo defaulted to factory settings, which is what happens if you disconnect the battery. However, the battery light is green. I don't know much about mechanics, but everything in this smells like a dead battery. Today it's raining so I can't do it, but tomorrow I'll take it out and take it to Advance or the Autozone to have it checked. What do you guys think? Can a battery show a green light but still be almost dead? I mean, could the system fail somehow inside the battery? Could it be a fuse?

Also, is there a way to open the hood of this car without releasing it from the inside? I'm asking because I have a neighbor that is a sleazebag and I think is a mechanic, so I wonder if this problem wasn't caused by him somehow. Two days ago I started the car without a problem and drove it for ten miles. And also, my wife told me the brakes were making a strange noise, and the brake pads are relatively new, and the master cylinder was replaced a couple of months ago. So can someone that wants to cause damage to the car can do it without actually getting inside the car and releasing the latch?

Thanks for any replies.

I would clean off the battery terminals and cable connections real well with some sandpaper and a wire brush. May have to jump start it if the battery is low. When it's running, look at the voltmeter to see if it charging okay up at about 13 or 14 volts. If you take it somewhere, it might be best to go by a battery shop. They could check all this, clean it up for you and tell you if the battery is any good by doing a load test. Could be just bad connections if there is some build up on the terminals. After that, Autozone can check for any codes.

I don't know if the hood can be popped without getting inside. I would say it would probably be fairly difficult. I have never tried it.