I ve optiplex Gx 620 3.4 dual core processor, can I upgrade processor In i3,i5,i7 , will motherboard compatible ?

I am able to power the laptop only with AC adapter, Battery is not charging, Battery indicator on LAP top is not ON. Task Bar Icon says 'On Ac Power' and batter is not charging. Any suggestions please ?

Does anyone know of a way to repair or replace this with something higher quality? I haven't had my laptop long and the chrome is flaking off and it has such a sharp edge it cut my finger nail just by brushing up against it wrong. I love this laptop, but the chrome strip is driving me crazy...