1973 Super Beetle

I just took my beetle (Little Greta) to a mechanic and had a new shifter put in and the brakes fixed. And I was able to master the manual transmission (yeah!)...so I can now drive her. Problem, though, she is having some problem where she refuses to start. I jump started the battery yesterday and she ran good for about twenty minutes. Then, today I went to start her again, but the engine just clicks and won't fire. The kill switch is turning on, though, reflecting that the battery appears to be working some and the lights plus radio work. So I jump started the battery again today and let it run; same thing once the engine is shut off; it won't turn back on..it just clicks when I press on the gas. As the car is parked in my driveway, and I don't trust the car to drive it to a mechanic; does anyone have any ideas what might be causing this? I thought it could be the battery, but now I'm curious if it isn't the fuel lines (she was having some symptoms of overheating prior) or if it isn't the starter or something. I would love any feedback you could give me along with the names of any good mechanics in Los Angeles area preferably on the west side or valley. Thanks! :)