MacBook battery won't charge, only partly recognized

I've got a mid-2007 MacBook with a replacement battery A1185 from 2012, running Lion (10.7.5).

My battery was only intermittently recognized by the computer, but for a couple of weeks, I've only got the "X" symbol in the menu bar. However, the computer could still work when unplugged, as it used the power of the battery it didn't "officially" recognize. Now that the battery is empty, it's not the case and I have to keep the MacBook plugged. I'd like to know what can be done to make it work again.

• I've reset the SMC unit a few times
• when the computer is plugged to the charger and when the battery is inserted, the Magsafe LED immediatly switches to amber/orange for 90 seconds (I got 3 minutes once). But there's no additional sign that it's aware there's a battery docked. Then the LED goes back to green. It's happening whether the computer is on or off. If I remove the battery, the LED goes back to green at once
• the computer could use the charge from the battery, but now that it's empty (I can't display any level by pressing the button on the battery), it naturally doesn't work anymore
• the battery is less than one year old, with ± 20 cycles
• it's the same with two different chargers. I haven't been able to test another battery

My guess so far is that it's a SMC issue (because it's happening even when the computer isn't on) but the usual SMC reset (power plug and battery removed, press 5 seconds on the power button, replug, boot the computer) doesn't work.

Is there any other way to reset the SMC unit? Can it be a logic board issue? Or a battery issue?

Thanks in advance...