Replacing battery went wrong won't turn on, any ideas?

My macbook battery had been swinging from "condition normal" to "service battery" so I thought about checking the connections/cleaning it up and also to inspect it for swelling.

I opened up the macbook and took off the battery. Apart from a bit of dust it looked fine so I proceeded to connect it back in.

As soon as I finished I checked if it booted and it won't turn on.

The battery indicator lights do not light up, connecting the power adapter shows only a dim green light on the adapter.

I tried also powering it up with the battery disconnected but and with just the AC but it does not show any sign of life. The adapters's light keeps showing only a dim green.

I checked also the battery indicator flex cable and it looks fine. I also tried a SMC reset by disconnecting all power sources and pressing the power button 10s but to no avail.

So, is a macbook mid 2010 or recent able to boot without a battery? - If so I might need a new logic board - or does it need a battery to boot? - this means I might be able to get it back in order if I replace the battery.