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In the past I changed the battery and everything went well. Now, the magsafe gives a green light but the battery doesn’t charge. I tried every reset procedure (i.e. SMC reset) but with no luck. Is it worth to try to replace the DC-in Power Board ?

At this point if the system is not able to start up your battery is not charging. You had stated the MagSafe charger LED is green. Is it a bright green or dim? Also lets clean the MagSafe connector port using a cotton swab and isopropyl alcohol making sure the buildup of junk in the socket is not messing up your charger. Post a picture of the MagSafe port so we can see Adding images to an existing question Here’s a good reference on what to look for Apple Portables: Troubleshooting MagSafe adapters