my guess would be the battery. if this is the first generation then the battery must be pretty old by now! If the LCD has a line on the screen of dead pixels then you will need to replace the LCD and digitiser... they come as one part and trying to separate them will only end in lots of tears. You could buy the parts separately and reassemble, then if one part breaks in the future you would only have to buy one (keeps costs down) I haven't included any links to the repair guides as you aren't sure which phone you have.. but they are accessible via the repair tab at the top of this page or by clicking on the step by step guides under the iphone photo. good luck.