Fan running on high, batter not charging

I was given a Macbook 13, core 2 Duo 2GHz in a dead condition. Wouldn't start, wouldn't charge. Charger light a dull green.

I changed the DC inboard. Got machine to start by using the method I saw on iFixit. Hold power button, with adapter off, for 10sec. still holding button, connect charger, hold for another 10 sec. release power button, then press once. It starts.

got 3 beeps at startup. removed one bad ram module.

Once booted, I reinstalled lion. keyboard, trackpad, wifi work. Fan runs full on. wont enter sleep mode by shutting lid, only by using apple menu.

coconutBattery shows nothing on battery, same with mac menu. I assume its an old battery and might be dead

Tried resetting SMU, but only way to startup is by the above method.

Is it worth buying a battery for? Or is something on the logic board not working. I don't know the history of it. But so far, everything seems to work. I also tried a power adapter from a macbook pro I have. Also shows a dull green.