The starting problem needs attention first, the rest is just cosmetic.
Get a digital multimeter from Dick Smith or somewhere ($20) and check the battery voltage, should be round about 12.5 volts. (12v and the battery is nearly flat).
When the car is running, test the voltage at the battery posts, should be around 14 -14.5 volts, if it is lower than this, your alternator is crap.
If that is OK, check for a parasitic draw on the battery - undo the neg cable on the battery and with a test light connect the cable, through the light to the battery post. If the light shines, you have a parasitic draw on the battery, you then start pulling fuses till the light goes out, that fuse will indicate the faulty circuit.
Try that first and let us know how you get on.
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