MB Pro won't boot up

Recently I tried starting my Macbook Pro and it won't boot up.

When I plug in the charger, the indicator light is green. On the computer itself the sleep light blinks a couple times a second, and it sounds like the a clicking sound inside.

I left it to charge for several minutes (10+) and still nothing. The screen doesn't come on at all, nor does the fans run. However, I noticed that after awhile the bottom of the unit gets warm (battery?).

I can't get a clear answer online. I fear it's either the logic board or bad ram.

If it's the ram that won't be too bad. But I have two sticks of 4GB in there, so it seems odd that both would fail at once.

I don't have any more to test and if I buy ones, it will cost about $75. So I want to be fairly confident it will work. And would it cause the computer not to boot up, not even the fan?

My other thought is perhaps the battery is such poor condition that it can't even hold enough charge for much of anything--maybe that's why there's the clicking, heat, and blinking LED, but nothing else happening.

I don't have an Apple Genius bar nearby. And this was bought secondhand, so there is no warranty. I actually had problems with it taking forever to boot up in the past, but I swapped out the hard drive and it has been running smoothly until now.