You've now two separate threads about how to fix a battery issue without replacing the battery, and how to repair a screen issue without replacing the screen.  The biggest factor here is that you're asking about a system that has a total value of between $30-50 complete and working. You can see if you can isolate the issue to the screen (hold the D key through powerup, which will initiate a screen diagnostic). If the same fault shows on the screen diagnostic, the screen needs to be replaced, plain and simple.  If it does not, the fault is either with the internal display cable, which can be inexpensively replaced, or it's with the GPU itself -- meaning a mainboard replacement. A replacement battery alone will exceed the value of the system.  Replacing a screen or mainboard on top of that will put you far under water as far as the value of the system. If you otherwise are happy with the system, check EBay -- you can find complete used, working systems for $30-50 or so -- total cost less than a single repair of this one, and you'll also have a set of other replacement parts on hand for the future.  
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How to fix Dell Inspiron n4050 white screen with vertical line