My 1972 is just plain acting wierd!

[irishiii]

Here is a rundown of my cars current ails-I'm not sure if they are all related to one issue or several different issues. Any advice is greatly appreciated:

For about two months the car does not want to start properly. I thought my starter was going out, it will turn over but won't catch and does the whirring thing. It will usually catch on the the third or fourth effort and once it starts it's running fine. Then one day last week it wouldn't start at all and my ex looked at it and said he thought my battery was dead. i replaced the battery on Friday and immediately after we put in the new battery the car refused to shut off. The key can be totally removed and the car just keeps on going. We have to get out and take off the air cleaner and push that little lever on the carb to make it die. Then I got in this morning to go to work and it's drained the new battery and it totally dead. EEK!

Okay here's the things I should have done and haven't, just in case they have a bearing on the problem. The car desperately needs an oil and filter change and new spark plugs and points. My ex won't work on her anymore and I can't afford or trust a mechanic. I have limited knowledge of my car (yes, I'm ashamed) because he always worked on her. Anyway, I let the battery run dry of water (who knew you had to add water, and btw how often do you have to do that?). Oh, I've been having some problems with the electrical, may be connected to the battery problem, sometimes I go around a corner or hit my blinkers and the radio cuts out-completely goes dead. I have a leak in the windshield (the painter didn't seal it right when he put it back in after painting the car and it's always leaked since) so water may have gotten down into the electrical system. I've really let the car go since the divorce, but it's because I'm broke and don't have anyone I trust to work on her. I'm in a panic because now she's not moving at all. I did take her out on the road Saturday, with the new battery, and drove about 90 miles round trip and it ran like a top.

Thanks in advance for any advice anyone has about what might be wrong or how I might figure out what it is!